Well Sliema is as good as any a place to stay. It is a fairly busy area, but has a fantastic promenade that runs all the way to St. Julians which is great for walking. Bars and restaurants to suit all tastes, but lively nightlife of Paceville only 10 mins away. There are good transport links by bus or ferry to Valletta where you can get buses anywhere on the island and at €6.50 for a weekly ticket it is by far the most economical way to get about.
You mention going elsewhere for a few nights, but you should note that Malta is a very small island and that might not be necessary. unless you want to spend a few days on Gozo.
For a first visit I would go with Sliema. Comment by TM001 spot on. As the island is small I would only stay in one place as you can easily get from one island to the other, and have to explore, in a day. Even if you opt to to stay on Gozo I would recommend going across one day of your holiday. Enjoy your planning and holiday.
Have you read the top questions about Malta on the top right of the page, especially where to stay?Edited: 26 January 2014, 17:54
Another recommendation for Sliema its so easy to get to everywhere from. I love the water taxi across to Valletta and its nice that if you do find an odd hour or two spare you can just nip across. Some lovely restaurants along the promenades too both on the views looking across the Valletta and also the prom along to St Julians. I am on my third visit and staying in Sliema for my third time.
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