Most if not all of these either have lots of teens hanging around or a bunch of teen programs/classes or both:

Brand new outdoor skatepark https://www.telegram.com/story/news/2022/08/21/crompton-park-skateboard-park-worcide-worcester-parks-recreation/10357227002/

Brand new indoor skatepark https://vesselskate.com/

Climbing gym https://centralrockgym.com/worcester/

Art museum https://www.worcesterart.org/

Gaming/comics shop https://www.thatse.com/

Music venue with lots of all ages metal, rock and hardcore shows https://thepalladium.net/

Pretty cool district with a public food market and a new baseball stadium https://bostonmanmagazine.com/polar-park-heats-up-worcester/ https://www.worcesterpublicmarket.org/

There a couple pretty big “gyms” under the name of YMCA that are really more like recreation centres with basketball, pools, Rick climbing, tennis and regular work out equipment, all of which usually have a lot of teens hanging out in one form or another https://www.ymcaofcm.org/news/events/mission-in-motion/

Having grown up in Worcester I can say that as a teenager I REALLY enjoyed hanging out at the 8+ (?!) colleges and universities to check out the concerts, shows, various programs, films and generally hanging out with college kids. https://www.worcesterma.gov/colleges-universities

Then, if you want to really dig in and depending on your interests there are some really cool places with teen friendly programs like Technocopia makerspace, Worcester Earn a Bike, 508 Bike Life

The Boston Globe recently had an article on how quickly Worcester is growing and adding new things to do and see https://www.bostonglobe.com/2023/01/30/business/worcester-is-booming-amid-bostons-housing-affordability-crisis-now-its-home-prices-are-soaring-too/