Day trip suggestions from Nice

A few years ago we spent two weeks in Nice, our second time there.
These were our favorite day trips , easy by bus or train:
Antibes- loved it. Picasso Museum.
Vence and St. Pail de Vence
*St.Jean Cap Ferrari and the Villa Ephrussi. Also walk to Villa Kryios, replica of ancient Greek home, very worthwhile. Love this whole area.
Villefranche- near Nice, have lunch there. Sadly cruise ships often moor there.
Monaco- go up to old town to Cathedral to see Princess Grace and Prince Rainier’s tombs. Visit Royal Palace. Then leave. Many tourists! We will not return.
Marc Chagall museum in Nice was built to house these special paintings. Wonderful.
We took buses along the water to all but Antibes. We would consider staying there next trip.
Nice- many art museums including Marc Chagall. It was built to

There is frequent train and bus transportation from Nice to Monaco, Eze, and Villefranche Sur Mer. In Nice we enjoyed strolling along the Promenade des Anglais, as well as by the port and the WWI memorial. Take the stairs to Parc du Chateau to Bellanda Tower for great views. The Old town flower market and cafes in Vieux Nice on Cours Saleya and seeing Place Massena were good also. In Monaco I would recommend seeing the Prince's Palace and the Oceanography Museum and you could have lunch at the Oceanography rooftop cafe. The Cathedral is nearby. Stop by Place du Casino to see the Casino and Cafe de Paris. Villefranche Sur Mer is charming with its lovely waterfront area and shale beach. The peach melba at Les Palmier is awesome. You could also see the Citadel. There is a bus from Villefranche Sur Mer to the Villa Ephrussi de Rothschild in St. Jean Cap Ferrat which is worth it. Have tea or lunch on the terrace there for great views. If you stop at Hotel Royal Riviera in St Jean Cap Ferrat you can walk along the Promenade Maurice Rouvier which has spectacular views. In Eze see the Jardin Exotique for eye-popping views. You will love the cobbled streets and stone shops in Eze. Stop for a drink at Chateau de la Chevre d'Or (Golden Goat) and sit on the restaurant terrace for the magnificent views. I hope you have a wonderful trip!

Dawn,
We have been to Nice 3 times, and the last time was for 1 week. (We also stayed a week in an apt. in Villefranche, once)
In Nice, you might like the Modern Museum of Art.
Or take a hike up The Castle Rock, and visit the cemetery. That may seem odd, but I find it an interesting way to really appreciate all the lives gone before us. Stunning view from the top, too. (There was a tourist train to take you to the top, but we hiked up)
Then, take a walk around the port side of Nice. There is a nice memorial to fallen soldiers on the walk over.
You might like the Chagall Museum.
The Russian aristocracy used to winter there, so there is a Russian Church, St. Nicholas, which is a bit of a walk from Old Town, and a little underwhelming, but it offers a different type of architecture, and an unexpected historical perspective.
And of course, the Old Town.
Last time, we stayed near Place Massena, where there is a lovely park nearby. And of course, the sea.
There is a Matisse Museum, but we weren't able to visit there.
A short bus ride from Nice (about 20 min) is Cimiez, with it's Roman ruins. Well worth the ride.
We have been to all the other places you mention, except Grasse. None require a guided tour, as they are small.
Villa Ephrussi de rothschild is lovely, however, without a car, I don't know how you'd get there. Maybe a bus goes there? (We had a car)
There is gorgeous trail, along the sea, from St. Jean Cap-Ferrat, near Nice. Again, we had a car, but maybe a taxi?
And you can take a short train ride to Antibes, a lovely old town on the sea. The Picasso Museum is there, too, but we didn't visit that.

We were there right after the terrorist attack in 2018, and there was a huge memorial in one of the parks, very heartbreaking)

Lots to see and do in Nice.

Enjoy.

Biot is an artsy community and a short train ride, then community bus.
Menton is great if you’re hankering for some Italian food as it’s near the border with Italy.
Others have already posted things I would suggest.

In Nice, try to sleep in the Vieux Nice neighborhood (old city). You also want to stroll along the Promenade des Anglais and also visit the Chagall Museum. Days trip suggestions are:
You can take a 15-minute direct train to Villefranche-sur-Mer.
Monaco-Monte-Carlo (30-minutes).
Ask about taking a tour of Cap Ferrat and Eze-le-Village.
Vence (1h 15m by bus but requires a transfer). From Vence you can take a 15-minute bus to St-Paul-de-Vence. To get back to Nice you’ll need to ride the bus again taking 1h.
Grasse (1h by train).
Antibes (30-minutes by train).

Thank you all so much for the wonderful suggestions :)

The scenic train into the mountains behind France and Italy is open, the Train des Merveilles. This is one of my favorites, going up the valley of the Roya.

https://www.ter.sncf.com/sud-provence-alpes-cote-d-azur/loisirs/lignes-touristiques/train-des-merveilles

These are all wonderful suggestions, savings them for my next trip. We went to Nice as homebase for Monaco and the grand prix, but never really explored Nice itself, can't wait to go back.

How about Menton, which has an Italian flair?

Filling in the blanks on the other responses:

Bus 15 goes from Nice to Cap Ferrat, with a stop just below the driveway to the Villa Ephrussi. The return takes you in a round loop through Beaulieu-sur-Mer. You can also walk around Cap Ferrat from this point, there is a path along the shore.

Don't bother with a bus to Antibes -- the train is much quicker due to traffic along that route (diminished this summer)

Train des Merveilles is currently FREE. The track was down due to Storm Alex and for the reopening they've made it free. From places like Tende, there are hikes that begin. This is at elevation, so even the weather in August can be variable.

For a taste of the water, consider the ferry from Cannes to St. Honorat. There is a large monastery on the island, with a winery. There are also short cruises to take from Golfe Juan (near Antibes) or the ferry to Sainte Marguerite.

These suggestions are wonderful!! Thank you all so much. I am going to do the train through alps and check on a hike in Tende. I am still figuring everything out, I am looking into all of these fantastic suggestions. Thank you all so much.

From Nice by public transportation I visited Eze, Villefranche, Monaco and Antibes. Very easy.

One of my favorite towns in France is Vence (and St Paul de Vence) but they are not easy by public transportation from Nice. I had a car both times I visited them. But I think it is possible by bus, just might require a little extra planning as to times.

I took the bus from Nice to St-Paul-de-Vence and on to Vence back in 2017. It wasn't difficult. My first stop was at the Fondation Maeght just outside SPdV, and it was a bit of a walk from there to the town; I think it was downhill. There was also a walk from where I hopped off the bus in Vence to the historic center; that might have been somewhat uphill. It's entirely possible that I got off the bus sooner than I needed to. Poking around on Google Maps using satellite view might give a clue about the terrain.

It's Lignes d'Azur bus LR 400 that runs from Nice to SPdV and Vence. Here's some schedule info. It appears that, at least on weekdays, the bus runs once or twice per hour. https://www.lignesdazur.com/en/route-schedules/6/RouteSchedules/nice-vence-par-saint-paul/1496/halte-routiere-lara-vence/1

I read Suki's post as the first one and Suki had it nailed. it's been awhile since I've been in Nice, but it's great. As others mentioned the Chagall museum is not to be missed. If you can take a bus to St Paul de Vence or Monaco--wow-that would be great. Nice also has a wonderful market full of local products and wares. Monaco may be easier to get to and it's really cool to see where Princess Grace was married and subsequently buried, and the yachts. The display of wealth in this tax friendly country is amazing! I loved St Paul de Vence and if there were an art watercolor class I could take, that would be where I would go--it's simply beautiful and very south of France. There is another little town on the way to Cannes, Biot--really cool glass blowing. The glass is unique due to all the little bubbles in it. Nearby Vallauris has wonderful ceramics and one of Picasso's famous works in a non descript building. Very super cool. If I were in your shoes, I'd hire a car service and do all of the above. You can easily do it in a day. Remember most places break for lunch for 2 hours. Plan accordingly.

Biot and Valauris are both accessible by public transportation. There's a Lejer Museum on the outskirts of Biot; the bus went past it. It might be walkable from the center of town.

I just noticed that you wrote second week of August. I'm in the south, near the coast and it's hot and the sun is beating down. If places close mid-day, there's a reason. So pace yourself. Get an early start in the morning. Have a nice lunch. Rest back at your hotel or in a shady area, cafe, park. Start sightseeing again toward 2:30-3. The temperature will start dropping around 4 and be pleasant until around 10 the next am. Don't forget a hat and water.
P.S. It will be too hot to hike up in Tende but the train ride is nice.