Hey Danae! I've been studying in Edinburgh since last September and one of the first thing I noticed was the welcoming atmosphere and lots of different cultures (at least 100 as far as I've heard).
In terms of the living expenses, most of it would be rent. There are rental properties with reasonable price pretty much in each part of the city, although Quartermile and New Town are considered more expensive. Zoopla is a great tool to find the place that is suitable for you: http://www.zoopla.co.uk/to-rent/map/flats/edinburgh-city-centre/?beds_max=3&beds_min=1&price_frequency=per_month&radius=0&search_source=refine
NOTE: in UK rental prices are often given "per week" (pw), but "per calendar month" (pcm) is usually also available.
In general, Edinburgh is quite compact city and the majority of commutes can be done on foot. Thus, the differences in cost of other aspects like food and sporting facilities are easy to overcome, if they exist.