As others have said, I'd opt for a drink with a view as opposed to dinner. There are fabulous restaurants in Athens, a bit out of the tourist core, and quite good ones even in the tourist center too.
For an unforgettable high end meal (which is reasonable compared to similar food in the US) Aleria is amazing. It's in a mansion with a beautiful patio.
On the other end of the spectrum, for fast food, the souvlaki at Kostas (2 locations - maybe more) can't be beat. There's usually a line, especially if you go at lunchtime as office workers get huge orders, but it's worth it. 1 -2 is a snack 3-4 are a meal.
and Ατίταμος is a great stop if you're walking to the Archeological museum, some of the best traditional food I've had anywhere for VERY reasonable prices.
Maiandros restaurant in the center is really surprisingly good given it's location.
None of these have views. We stayed at a hotel with a rooftop bar with a view of the Parthenon and that worked great for us.