I’m unsure of your price range, but if 70-120 euro sounds about right then try Hotel Plaka. It’s an OK property are rates start at about 116euros, not too over budget. The people are courteous, perfect location hotel in the center of the action. Just keep in mind it’s not an Deluxe hotel.
The name suits it perfectly because it is literally on the doorstep of the Plaka. 5 minutes walk to Syntagma, the National Gardens, 10 mins to the Acropolis. Rooms are clean and quiet with minimal frills. All have tv, ac, bath, shower, and phones. Prices include breakfast, and the staff is generally very helpful for your everyday needs. There is also a nice rooftop garden/lounge area that has spectacular views to the Acropolis.
You can find much fancier and probably cheaper, but for location, convenience, and price in the Plaka, this is one to look at. If that is to much $, try Hotel Metropolis. It is on Metropolis Street about 3 blocks towards Syntagma from the Plaka Hotel. You can get rooms with shared bathrooms or bathrooms that are included. The rooms are very clean if a bit small.
In the Hotel Attalos 70 euros for a double room with bath and breakfasts. It is a few minutes from Plaka, the Acropolis and the Ancient Agora.
Astor Hotel is just about in your price bracket and is just off Syntagma Square. It’s as good as old city center hotels go. Rooms with an Acropolis view seem to be the last for refurbishment. Ask for one at the back and rely on the dining room on the roof for the spectacular view.