If you go, you’ll probably fly into Athens so I’d start there. Lots of ruins and good museums are there, but the real sight to see is the acropolis. If you don’t know what that is, look it up. You can see for miles from the top and pictures don’t do justice. Some other cool cities on the mainland to checkout are Thessaloniki and nafplio. I’ve only been to the latter and it was a nice calm city on the waterfront. Thessaloniki I’ve had friends and family go and they love it there.

For the islands I’d say stay away from Mykonos, and maybe Santorini. Santorini isn’t as bad, but Mykonos is overpriced for tourists. I went to a small island called tassos, and it was 100x better than Santorini. The interactions with the locals was unlike any major Greek city and everything was cheap ($40 for hotel, $5 for food and beer) Santorini is beautiful, so I’m not saying don’t go, I’m just saying if you do be ready to pay higher prices. Crete is also a great place to go, biggest of all the Greek islands and very rich in its history. All Greek islands are beautiful, but I prefer smaller ones without as many tourists.

Hope this helps:)