Hello
Yes, my Mum lives up in Qawra, one of the touristy towns on the island's north coast.
If you want to avoid clubs do not stay at Paceville/St Julians. It's the night life centre for the island and can get quite rowdy.
Qawra is good, lively enough to enjoy but not so loud for it to be too much, many bars/restaurants. etc. Buggiba is the ajoining town to Qawra and is a bit like Blackpool in the med. If you want a holiday with all the brit trimmings it'll do you proud!
Don't worry about transport, the buses are excellent and conveneint, you can cover the island from end to end in less then 45 minutes.
Based on what you are asking for try looking for Hotels in Mellieha bay, Qawra (NOT Buggiba) and Valetta. There is an awesome hotel in Mdina called the Xara Palace, referenced further up the thread if you have the cash, it's stunning.