Majorca is about the size of Essex. There is one very big town (Palma, 400k people), a few other inland towns (5-50k people) where not much happens, and then about 15-20 large-ish seasonal holiday resorts.
None of the other inland towns have any tourism infrastructure to speak of, nor would you go there for a week's holiday without a car (or a plan to tour by bus, which is actually quite do-able). Yes, Manacor has the Rafa Nadal Experience, but that's just a fun half-day out for people who like tennis. Pollensa and Andratx are beautiful to walk around, but only for a day, unless you're a writer or something. In fact apart from Palma none of the towns take more than a day to explore.
The good news is that the seaside resorts come in various degrees of liveliness/niceness, from Magaluf (lots of stag/hen dos) and Arenal (lots of German stag/hen dos) through family resorts like Alcudia and Santa Ponsa (lots of AI places, no shortage of football shirts or full English), some more relaxed places with fewer Irish pubs (Puerto Soller, Puerto Pollensa) and on to some quite posh places (Port Andratx, Portals Nous — think Howards' Way, updated) and then some very quiet ones with not much to do after 10pm apart from finish your brandy and watch the evening twilight over the water (Portocolom, Sant Elm).
So your main options to "chill and sightsee", depending to some extent on the composition of the party and your budget, are either (a) a hotel in the countryside (there are some nice luxury places), with a car, and either a non-drinking driver or judicious use of taxis for those evenings where you don't want to eat in the hotel's restaurant; or (b) staying in one of the quieter seaside places and getting around by car or bus.
Or of course, stay in Palma. 😎