Best country in Europe to daytrip Monaco from??...

Stay in Nice.

I thought that Nice was pretty expensive, given that it’s on the French Riviera.

Monaco is a tiny little thing surrounded by France on all sides, but Italy is about 10 kilometers east, all connected to Monaco by rail. You can check booking.com for Menton, France or Ventimiglia, Italy to get a sense of the prices. We don’t know your price range. The Riviera has a wide price range; it’s not just wealthy vacationers or residents.

$50-$100 per night, for one adult, is the price range.

Menton is more of a family friendly place. You might get better prices there.

Check out Hotel Solara in Nice. It's not on the waterfront but is on the pedestrian only street that leads to Place Massena, where you can get the tram to the train station. It's also just a few minutes walk to Old Town and to the Promenade Anglais along the waterfront.
It's a great location and a nice clean hotel with friendly staff. It's around $100/night for a single/double, no breakfast included. I took the train to Monaco for 1/2 day - cheap, fast, and easy. There is also a bus to Monaco.

OK, thanks for all of the replies!

Nice is probably going to be the most expensive place to stay in. We were in Nice last summer and we visited Monaco as a day trip (can't say I'd return, I found it very boring and the much touted aquarium was absolutely packed so you could barely see anything and it is actually quite mediocre in comparison to many other aquariums I've been to). We also took an easy day trip to San Remo in Italy and whilst it may lack the glitz and glamour of Nice it will certainly be less expensive.

To answer your specific question, I recommend France.

We stayed in Nice as we found plenty of inexpensive hotels from which to choose. We took the train to Monaco for a day trip. So easy to do.

You don't say when you're going. If it's in summer prices will be higher, so you may need to adjust either your budget or your expectations. Any town right on the coast will be more expensive than one that is inland. We wanted something quieter than Nice, so we stayed for several days in Villefranche Sur Mer. Then daytripped to Nice, Monaco, and a couple other places.

France would be the best country to daytrip into Monaco from, with Italy second.

Price is not necessarily prohibitive from staying at Monaco, I've done it frequently. €35 will be very tight though, anywhere in western Europe. Have a look at Beausoleil, the suburb in France walking distance from everywhere in Monaco (or frequent buses) where the cheap hotels are and the many many workers who keep Monaco running live.

dave,

I'd also suggest staying in Nice, as it's a beautiful city and makes a great home base for touring that area. Unless you're planning to spend all of your time in Monaco, that's a good choice. As I recall, there used to be a Bus from Nice to Monaco for €1, which drops passengers at the bottom of the hill. From there you can either walk up to Monaco or take another Bus for another €1.

Have a look at the RS France guidebook for all the details.

I'll add another vote to stay in Nice. We spent 2 nights there at the end of our tour. Beautiful area and wonderful cuisine. We took the bus to Monaco and enjoyed the scenery, saw the changing of the guard, & visited the church where Princess Grace is buried. We thought it was a worthwhile day trip.

I also recommend the Hotel Solara in Nice .

We found it clean , comfy , had good ac , and super kind staff ( desk clerk phoned around for us to find out some information we needed ) . It’s odd in that it’s in a residential building on top floors , we also had a nice balcony . Good cheap food at cafe across street .

We stayed at ETAP hotel (now IBIS Budget) in Menton and took a train to Monaco. Nice waterfront location, 1 km away from the Italian border and also close to the railway station to go to Monaco or San Remo (also highly recommended). There were also some nice and not too expensive restaurants nearby.