Depends on your budget
They like hoodies and trainers if you want a retail therapy day
Any local theatre/comedy?
There is a new deadpool/wolverine film that is likely to be rated 15, if you haven't seen deadpool 1&2 you might like to watch them together first, but be warned if you are easily shocked it's not for you, it's brilliant but it'll crass, rude, offensive, violent, just plain bad and has a leading connection of loss via death.
You would need to check with dad first.
Can you/he play chess? You could get a chess puzzle, so part game and you work out the "checkmate in 3" solution
Bird of prey day
Archery
Go karts
Bowling
Photoshoot somewhere with good backgrounds
Any fairground rides about?
A day climbing something for a view
I would have a look around at where you can get to and what you need to book in advance and what you don't. Perhaps take him out locally first day, even to supermarket and say get some food you like for a couple of days and see if he has any suggestions.
Or if he is arriving to late on first day or you just don't fancy it, cheeseburgers, ice cream, Oreo biscuits tend to work
Lucozade sport drinks
15 year olds like choice but perhaps with a gentle nudge in the right direction
Indoor skydiving
VR arcades
Actually most arcades
You and him both have you sister and your loss of her in common. I would assume, once he is feeling comfortable with you, and if you feel you can, he might want to talk about his mum.
Get him to show you what he likes on youtube it might be quite good or utter toss. Feign an interest!
I hope you both have a great time together.