I have to say, I'm not too big on relaxing while on holiday. I think that probably has to do with the fact that my normal schedule and routine is so simple, and demands so little from me. When I get around to going on holiday, I'm itching to do things. And to eat. Actually, one of the things I love about traveling in Japan is that most every little town and village has a local delicacy of some sort, and they're usually worth trying. Unless it's natto or crickets or bee larvae or something.
And, in general, I have a basic inability to be really comfortable and relax if I'm not doing something important or productive. I know this is an unproductive neurosis, and I do try every so often to work on it.
So, usually my holiday MO is to start out with a flurry of activity, including lots of walking randomly, and then gradually wear myself out. Then I'll take it easy for a little while, and then go somewhere else and wear myself out again. Repeat until trip time is exhausted, then go home to rest up.
As to traveling with others, I really can't say, as I've just never had the opportunity. I'll likely get around to trying it sometime, but who knows.