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/

Pizzeria Uno and the Mexican place, both directly across the street from DCUBare both solid choices for that age.

Dealers will weld a plate over the CC making it essentially impossible to cut off with sawzall. Costs a couple hundred bucks.

Need to check local regs. Most larger MA cities/towns have a full ban on burning yard waste at all times for both safety but mostly air quality concerns. The definition of a cooking fire in these towns is very narrow for this exact reason. But those cities, such as Worcester, have yard waste drop off sites.

You should probably do a little more homework on your tax situation. NH is technically a functioning state and has to pay for that function with some form of taxes. The result is that NH has the 4th highest real estate tax in the country. And if you earn your income outside of NH, in MA for example, as many NH folks do, you’re paying income tax in the state where it was earned, not NH.

I can’t tell you how many MA folks I know who moved to southern NH to “avoid taxes” but ended up still working in MA and ended up paying a much higher effective tax rate, kind of the worst of both worlds between real estate and income tax.

https://smartasset.com/taxes/new-hampshire-property-tax-calculator#:~:text=New%20Hampshire%20is%20known%20as,tax%20payment%20here%20is%20%246%2C097.

https://vesselskate.com/ indoor skatepark is likely your best bet in winter weather

https://www.youdoitelectronics.com/ in Needham is what you’re looking for

It’s a pretty high crime area. If it’s just you, don’t plan on walking around all that much and don’t have a nice car, you’ll be fine.

You’re going to school at UMass?