Hi Shinypurple and welcome to the forum.
I've moored at Nottingham Castle marina. I enjoyed my time there. The management are friendly and helpful. It'd be a great place to get used to a boat as there's pretty much all the facilities you could want on site (toilets, showers, laundry, elsan, pumpout, diesel, coal, gas, chandlery, slipway and covered wet dock, etc). David Mawby offers blacking at a reasonable rate and there other folk there that offer painting and mechanical work if needed.
The marina has secure access and car parking is very close to the boats. The site is surprisingly very quiet - so long as you don't take a mooring near the main entrance end. There's a good sized Sainsburys that's just five mins walk away. There's also couple of chain pubs, restaurants and fast food outlets nearby too. There's a Premier Inn very near the marina as well.
Nottingham has a large busy centre with loads of shops plus cinema, theatre, museum, ice rink/events arena, and many, many places to eat - there'll be plenty to do for a teenager. It's about 20 mins walking from the marina along the towpath right into the town centre (watch out for speedy cyclists). There are some busy canalside pubs in the centre and like most big towns the canal side in town feels like a bit of a different place after dark.
For weekend cruising - a few folk like to go for a short trip through the town centre then turn right onto the Trent and spend the weekend moored on the steps. Going the other way, turning left out of the marina, there's some really nice cruising along the Nottingham and Beeston and then out onto the river and heading upstream to wherever takes your fancy really (junction with the Soar/Erewash or carry on to the Trent & Mersey - just depends how far you want to go in a day I suppose.
LCx