Athens

You can buy tickets to visit them online on your own. Less expensive in winter months. Free on certain holidays. I have gone there twice on my own without a guide but did have a good guidebook.

The area has a lot of hills, but they are all kinda in the same area. I did an uber and it hooked into the Taxi network(like 6 euro either way with tip). Make sure to bring your passport and vaccine card. I had to backtrack to the hotel for mine!

The Acropolis Museum is at the base of the Acropolis. It is a good 1-2k walk to the base(from the museum area), then a lot of elevation gain to get to the top. The nice thing is you catch the Roman Agora at the base on the way.

It is all safe, except you will be in a touristy area. Caveat: that Greek sun and humidity is rough for the first few days. Just a heads up, you will hear a lot of angry complaining tourists up top.

For a great guided tour of the Acropolis find FAYE GEORGIOU.

Another enthusiastic vote for Faye Georgiou. She was our great guide for the museum.

The best way to experience the Acropolis is at opening time at 8 a.m.

You'll have a good hour of relatively peace and quiet before the tour groups and hordes of tourist show up.

Another option is late day after tourists have gone.

If you want to see the museum go down the south slope to explore more of the site and eventually you'll go out the exit very close to the New Acropolis Museum.

There are various prices for tickets for just the Acropolis and a separate cost for the museum.

You can also get the multi-site ticket for 30 euros which will get you to the Acropolis, Agora, Hadrian's Library, Temple to Zeus and Kerameikos Cemetery, one of the most under rated sites in Athens.

There's cheaper and there's more efficient. If you have limited time, I recommend spending a bit more and saving precious time. The National Archaeology Museum is a Wow, but it's a bit out of the center. Splurge for a taxi/uber, otherwise, you may have a bit of a walk, or get a little lost, or wait too long for a bus/tram in one or both directions. You can't take backpacks into the museum so leave them behind or check them. If you can, buy tickets in advance to avoid the line.

There's a combo ticket for the ancient sights, which is probably worth it just to avoid waiting in line at each sight, though you may not see all of them and may not save any money. The lines at the Acropolis are usually the longest. The Ancient Agora was my favorite.

I'd rank the Acropolis Museum as a second tier sight, but the view from the rooftop is worth a visit and the restaurant prices are reasonable. You don't have to enter the museum, just go straight up and enter through the bookshop. You can go out to the terrace to admire the view without patronizing the restaurant.

The RS walking tours were very good.

If you have no background, Here are some options for various places:
ACROPOLIS -- one option is taking a good group tour with licensed guide like this - http://www.athenswalkingtours.gr/ - it starts a bit earlier than some others, so beats the crowd by a little. However I think it's about €30, and yu WILL be with about 25 other people. If you want to go on your own, at a less-crowded time of day (at very opening 8:15, or from 4 pm on), Rick Steves offers a FREE step-by-Step podcast (Click on "watch read listen on LH side of page) to the ACROPOLIS, download onto your phone.

ACROPOLIS MUSEUM - does NOT have a podcast guide, but it's well-signaged, & has "docents" scattered around if you have questions. If NO background I suggest FIRST taking escalator to top floor, for a super 20-minute video giving complete background & history for understanding Acropolis & Parthenon. After you work your way down, the terrace restaurant is great for a moderate-price salad or sandwich, looking right up at Parthenon.

ANCIENT AGORA -- Many people go right into this Acre of Ruins when coming down from Acropolis/Parthenon... and it can be fascinating IF IF IF you know what you are looking at! Luckily again, There's a FREE downloadable R. Steves Podcast that steers you around the high points, including some gems in the (authentically restored) Stoa of Attalos -- which is devoted to all the treasures that were unearthed when the Agora was uncovered in the 1930s-1950s.

NAT ARCHEOLOGICAL MUSEUM - One of true wonders of Ancient World. You could get lost for Days. Luckily, R. Steves also has a FREE downloadable podcast of "10 top highlights" of Archeological Museum. IF you are staying in Plaka area its quite a long walk to Museum; taxi is about €5 + tip (ASK driver befdore you get in)... walk back if you have leg-energy left.

.... finally, I cannot urge you enough, please do a bit of advance prep. Some people think they'll grasp the significance of a site (OR a country) by hearing the spiel from Cruise-group leaders. Those folks give you the kindergarten version, sprinkled with corny jokes. When you do even a little homework, these landmarks will resonate much more deeply.

Thank you all for the advice! Yes, I do a ton of research before I travel but I like to also have experts add to that. Always open to learning more, especially from locals!

Lots of good advice. I second tommyK get to the Acropolis at opening. You can buy your multi site pass at the Acropolis ticket office. By arriving at opening it will still be somewhat cool which is good and there will be far less in the way of crowds. You will have a good hour before the tour bus crowds arrive. This would be a good time to leave and go to some of the secondary sites.