Last time I was there I stayed at the Caribbean Paradise Inn... small place with a low-end free breakfast by the pool, internet etc... Wasn't bad, 100 yards to grace bay, walking distance to Jimmy's Dive Bar. If you're there for 5 days you may want to try something on the beach with a little more going on.
You can use jitney's to get around on the island. Usually $2/pp one way if you don't mind hopping in a strangers car. Island is generally safe from all I've seen. Provo Air Center will take good care of you down there. Nice Island, just not a lot going on.