As a resident of Athens, please let me put forward my 2 drachma worth.
Avoid the Melia. The location is in probably the worst part of Athens a tourist could be stuck in. In fact avoid Omonia all together.
As many of the excellent suggestions above have alluded to, the best place to stay are the areas called Syntagma and Plaka. Both are very close to the Acropolis and other sites as well as great bars, restaurants, tavernas, cafes etc.
Avoid Piraeus as well. My office overlooks the harbour but that’s about the only thing the place has going for it. Unless you know where to go, you could end up getting stuck in an awful area.
The Hilton is great and only 1 metro stop from Syntagma square. It’s like a mini resort in the middle of an upper middle class inner city suburb and has a great pool and impressive, yet severely overpriced bar – Galaxy. Alternatively, anywhere in Kolonaki is great. It’s the high end shopping area of Athens. There are plenty of great hotels in the area.
There is also great boutique hotel called New Hotel which is centrally located and has a great rooftop bar worth visiting. Same goes for ‘A for Athens’.
I haven’t mentioned many specific hotels as I find getting onto a accomodation booking site and seeing the photos usually helps. Hope the location recommendation helps though.
As for dinner, try the Thissio area next to Plaka. Great views and a nice choice of restaurants with outdoor seating. And for coffee, visit the Lycabettus Hill. has a cute church on the top with a lovely cafe next door. Highest hill in Athens and has breathtaking views. It’s in Kolonaki and close to Syntagma Square.
Any more question, feel free to ask. 😉