Edinburgh was built on a hill - seven of them, in fact - but walking is still one of the best ways to get around and a great way to take in the city from the windswept slopes of Arthur's Seat to the narrow wynds of Edinburgh's Old Town.
The city is relatively compact, so if you are staying in an Old Town hotel or a New Town flat many of the cities attractions are on your doorstep, including theatres, cinemas, bars, clubs, and restaurants. Popular residential areas such as Stockbridge, Haymarket and Murrayfield, or Newington and Southside are but a brisk twenty to twenty five minute walk from the city centre.
A general perambulation is without doubt the best way to discover the nooks, wynds, hidden closes, stairs, and crannies of the Old Town. You will see stuff that you wouldn't from the top deck of a tour bus, via Google's streetview cameras, or by bicycle (unless your name is Danny Macaskill).
For more pastoral walks, there is the Water of Leith, Calton Hill, and other Edinburgh parks.
For longer trips, there are a fair amount of public transport options - buses, trains, and in coming years trams.
Edinburgh also has a good off-road cycle network - although few of these are in the city centre - and plenty of black cab taxis.