I visited Hanioti in June with my girlfriend and didn't have a bad meal once. There are loads of restaurants to choose from on the square and down the surrounding streets. We personally enjoyed Gustos Italian (great pizzas), Prime (the owner recommended his traditional greek dishes and offered to give us our money back if we weren't impressed - we were!), Amethystos and The Garden.
Also look out for both The Hot Goblin shops. One does fantastic jacket potatoes (massive) and the other tasty fish and chips if you're missing your traditional english scran. If you want a traditional english breakfast try The Old Tavern. We found them to be the best.
As for good bars, we were staying at The Hotel Angelo so usually started the night in Waikikis. Our favourites around the square were Long Island, Kelfos and The Sunshine Bar but we generally just when in the one that looked the busiest.
Hope this has been some help but I'm sure you'll find your own favourites. You can't really go wrong!
Steve