Hi there Coder,
You've received offers from two very good and respected unis (congratulations!) and I'm sure you will have a really great academic experience at either. I can't personally speak for Kings', but I'll try and help with the Bath side!
What's most important is that you pick a place based on which course you'd rather study - which better suits your interests and where you want to be in the future? This is a key factor in your decision as this is the main investment in the next 3-4 years of your life.
I would also consider whether Kings' has a placement option; because at Bath, we have one of the best industrial placement schemes in the country with the huge majority of our courses offering version with a year-long placement (Robotics included). This is not only the chance to do something fun and different for a year, but its a chance to earn some money, try out a new career and get experience which will add so much to your graduate CV.
On living at home VS moving out I agree that when you live at home it is not as natural that you'll run into as many people and so you'd have to make extra effort to be on campus, get involved with things and join clubs etc, but this is perfectly doable - I lived at home and commuted to Bath in my second year and found it fine 🙂
Personally I really loved my time at Bath. Its a smaller uni than Kings and so feels more like a small village, with a lovely open and social vibe. Bath is also a much smaller city than London with a slower pace of life (also one of the safest cities in the UK!) but considering, it also has a lot to do - plenty of pubs, a few cocktail bars and nightclubs, green parks, a shopping district, independent coffee houses and street food joints, and is a great, welcoming place for students. Have you had the chance to visit it yet? What did you think?
The main pieces of advice I'd give you is to A) choose which course you prefer, and B) definitely consider the placement option because it is so valuable afterwards, and C) choose where you think you will be happiest and lead the most fulfilling student life.
I hope some of this helps but please give us a shout if you have any questions! 🙂
Holly
University of Bath