Edinburgh is pretty easy to get around on foot, although it can be quite steep in places. It does have a really good bus network though and you'll get to try the much hated trams The castle is minutes away from the train station on foot, as well as the parliament and dynamic earth but the zoo and deep sea world are on the outskirts of the main town centre. I guess it depends on what you want to see but all the touristy places are really close to the train station/bus station.
Is Edinburgh a decent spot for a mini break, especially when one would be relying entirely on public transport to get around?
I'm more of a Glasgow fan myself but Edinburgh is really nice, some lovely photo ops on Arthur's seat.