Most places in London you can get to by tube or bus so you do not have to worry about driving, unless you are looking at zone 4 or 5 or further.
A river view may be a bit more difficult to get, assuming you budget isn't a lot as you mentioned you are studying I do not think a river view may be in your budget but I may be wrong? If it is in your budget then Tower Bridge, St Katherine's Dock, near Waterloo may be your choice. Most of these places are relatively safe.
If your budget is restricted then I would say East London (Whitechapel, Aldgate, Aldgate East, Tower of Hamlets) there are a flats that are a reasonable price. They are in zone 2ish and most have pretty good bus routes to Tottenham Court Road. I am not sure if there's a direct bus that goes to Goodge Street but if you are not scared of walking, its not too far from Tottenham Court Road.
Marylebone is a nice safe area and not too far from UCL on the Marylebone road, but prices are quite high but there is a chance you can get lucky depending on the market. I would suggest trying places like Blackkatz or Flatland London as you only have a one off finders fee and then viewing and contracts are dealt with the landlords directly. I found my first place through Flatland, admittedly it was only a bedsit but it was just off Marylebone High street (5-10 minute walk from Oxford Street) and £550, so its the luck of the draw. I will admit people have had mixed feelings about the above two agencies, so its worth doing some research on Gumtree for the going price in a certain location before signing anything i.e. make sure you are not paying above the odds in a certain area.
All the best with trying to find a place