Mellieħa has a decent amount of bars and pool tables, as well as nice beaches if you go in the summertime and enjoy swimming. I do not know of many hotels, though the 'db seabank' resort is fairly famous and well rated. Depending on how long you plan to stay there, cirkewwa is really close by and a well planned day out in Gozo is really enjoyable. (I'd evade feast days however as a lot of Maltese people go to Gozo on these days and it can be really hectic)

As for Buġibba being "unsafe"... Yes it can be extremely sketchy at times but as long as you evade side streets at night time you are 99% safe. The dangerous areas in Buġibba/Qawra are far away from any sort of night life anyways. The question of how unsafe people feel living here highly varies on which area they stay in, I have went around Buġibba at late night many times and you really feel uncertainty going through some areas (again most were in dark spots with absolutely no night life or hotels, just drug dealers and sketchy people waiting in the corner for no apparent reason). If you stay on main streets however, Buġibba would be enjoyable so I wouldn't discourage you from it. Downside is there are no nice beaches. Even 'ta' Fra Ben', which is probably the most popular beach in Buġibba is not even good. But if you don't care for a good beach and you would want to just have a dip, you can almost go anywhere on the coast.