You're probably going to have to compromise on some of your requirements. Almost no places that meet your description will let in anyone under 18 (much less 21) after dark. You could maybe find some pubs in the afternoon who'll have live music, but I'd temper expectations.

Aeronaut Brewing up in Somerville might be your best shot, but it's a significant walk from the T. They have games and live music on the weekend and they allow all ages. You could try some jazz spots like the Beehive or Club Passim, but they're kind of stuffy and maybe not great for teens who aren't already in to jazz.

Is this puppy house trained? If not, you're going to need someone to come by 4/5 times a day while you're at work and provide the service of training the dog for you. They're not going to just do the latter for free.

If this is the case, you're better off finding someone to leave the dog with for the day and pick up from later. Puppies are a lot of work. It's not something you can easily just outsource.