I replied to a similar question on another forum I frequent, I've pasted my reply here to save me typing it out again....
I have recently sold a villa in Mellieha, and holidayed there three or four times a year for the last twenty odd years so know the Island well. Malta seems to divide people, they either love it or hate it....naturally we think it is lovely.
Best time to go..(in my opinion) is April/May....September/October....UNLESS you like it very hot..then go(June/July/August).
Personally, I would not go to Gozo for a week, it is fairly quiet, very small, and not enough to do there for a week...take a day trip though on the ferry..(30mins) and see Xlendi Bay, Marsalforn, Ramla Bay and the capital Victoria.
Best beaches on Malta?
Mellieha and Golden Bay.....Google them.
Also Google these places:-
Mdina...(Pronounced Imdina)
Armstrong Gun, Fort Rinella...(Saturdays)
Malta Drag Racing
Malta Car Museum
Mosta Dome
Valletta Grand Harbour
Paceville/St Julians
Sliema
Bugibba
Captain Morgan Cruises.
Sunday Market at Marsaxlokk...(Excellent..get there early)
T'Quali craft village
Comino
Malta war museum
Blue Grotto
The Maltese are extremely friendly, all speak English, prices are generally similar to the UK, AND they drive on our side of the road. Car hire is reasonably priced...hire a very cheap car, you do not need a big fancy one, the island is too small.
If you like nightlife, Paceville is where the action is.