You need to find out exactly where the villa is in relation to the old town, it could be on the road to Puerto Pollensa, or into the countryside, if you are going in the summer hols you would not want to walk as the roads are very busy and its too hot! The old town apart from the city walls is not very inspiring, not much to do at all, the port of Alcudia is literally straight down the road but it is a LONG road and again not reall y walkable. Alcudia port is very busy, lots of nightlife, if thats what you want. It does have a fantastic beach, but far far better is to go to Puerto Pollensa next door, fantastic family place!
We weren't too inpressed with Alcudia old town, like triplets says there's not much to do. We went on market day and the stall holders were to pushiest I have ever seen! We stayed in Alcudia, but about an hour's walk from the old town so we decided to get a bus in. THE MOST scariest bus ride I have ever taken! They packed us in like sardines with hardly anywhere to hold on to, and it was roasting hot and you got jerked around all over the place!