there’s a good deal of stuff to do but I wouldn’t let a 15y/o wander around certain parts of worcester. My go to activity is actually taking the commuter rail into boston or natick (the natick mall is really nice and they have an arcade). the Massachusetts train system has a weekend pass that lets you ride the commuter rail as much as you want for 10$ on saturday and sunday. Within Worcester theres a couple of strip malls to go to but nothing particularly interesting. The library we have is actually pretty nice and they give out coupons that you can use at popular Massachusetts museums/zoos/aquarium. If your mom drives you theres a lot of stuff in the surrounding area too (ice cream, movie theatre, etc). My only advice for you personally is to be careful where you walk alone, and to avoid the homeless in worcester. Most will leave you alone but theres a couple of nasty ones that will pickpocket or aggressively follow you around for money (like 20$, not just pocket change) and you can never tell which are which.