During my first walks around Prague Castle some years ago, I noticed many pretty gardens below it, but I thought they’re private property, no trespassing, etc. Luckily, I was wrong, as there is historically formed connected belt of greenery gardens available to public, and these are: Ledeburg Garden, Small and Great Palffy Gardens, Kolowrat Gardens, and Small Furstenberg Garden (Great Furstenberg Garden is being reconstructed and is not open to public)
Actually, these gardens are not only open for walks, but also for private parties, concerts, weddings, etc. I will not write much about their history, I just want to mention these sightseeing gardens offer really nice view of Prague panorama, and can be a suitable place to walk and relax in this lovely cultivated area.
On May, the gardens are open from 9 to 19, next summer months even longer. The place is right in the centre, no need to travel far, the address is Valdstejnske namesti 3 (very close to metro line A Malostranska). And to mention the entrance fee, it is 79 CZK (49 CZK reduced), and optionally, 20 CZK to Ledeburg gallery.