One of the best thing about Edinburgh is that even though it is not a cheap city, the views are free and there are several places from where you can get a great view of the city. One is Carlton Hill. North East of the Old Town.
Unfortunately, construction on one side of the foot of the hill muddies the vision of the Georgian New town but it is still a great spot for sightseeing. It is an easy but vigourous walk to the top.
The hill is also home to a number of monuments, and sights including Edinburghs Nelson Monument and the original Edinburgh Observatory (shortly after opening it was realised that the lights and haze of the city obscured the view of the stars and it was moved).