I'm not sure what you consider reasonable, but we really like the Hotel Albergo del Senato, centrally located & literally right on the plaza by the Pantheon: https://www.albergodelsenato.it If noise bothers you, ask for a room that doesn't face the plaza -- if you like seeing the activity (there are always musicians in the plaza but not after 9 or 10pm), then try to get a room facing it. They also have a great roof deck bar for those staying at the hotel. And only a block or two walk from some really great restaurants.
If you want a quiet, removed place (doesn't sound like you do) in a residential section of Rome (up on the Aventine "hill", but walkable to the center), we like the 3 hotels owned by the same people: http://www.aventinohotels.com All reasonably priced, each slightly different.
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