Apart from what I said. The places I think are really nice are in West London but can be a bit pricey are
Chiswick,Hampstead, NottingHill, Holland Park, Regents Park, Sloane Square, Richmond, Knightsbridge, Kensington, Hyde Park, Victoria..
But the more west you go the more you might need a car and the train prices increase.
Also alot of young professionals are moving to Putney recently (more south). There is nice too. Also nearby Fullham can be nice too.
Richmond/ Kew gardens is very pretty but kinda far out. More suitable for families . As not much to do.
Some parts of Wimbledon are nice too if you like green.
Pimlico is also nice in some areas.
I think Clapham is overrated but popular and good for going out.
Warwick Avenue is very posh but nice too .
Angel and Camden area is also popular with young people and students . But Angel is more expensive. It is nice there. Camden is very crowded on weekends with students but alot of places to eat and markets on weekends. Barbican and Farringdon are nice too. They are also close to this area.
Highbury is nice too but a bit far out. It is where Mr. Bean used to live in the actual Mr. Bean show. haha.
Maryleborne and Baker street area is nice too.
Chalk Farm , Belsize Park is very very posh. Where alot of rich people live but you can find affordable too.
I honestly don’t recommend living in very East london but you can save alot of money by living there.But there is nothing to do on weekends and if takes a long time to get home if you go out . Don’t liver further than Aldgate east in East London. I think nicest places in East London are Shoreditch and Aldgate for students as you can go to Brick Lane market on weekends and also nice places to hang out in shoreditch.
You can live in Canary Wharf in East London which is the 2nd financial district. It has alot of modern apartments but I think it is too far out and more for professionals that want to be close to work.
Ok enough for now. ha
If you are just going as a student it might be a nice experience to just get a really small apartment or apartment share in a really nice area in West London . That way you can experience the nice parts of London and will have fond memories except for the size of your apartment ha !!