This is my first post here as I live in Salisbury and felt informed enough to reply. Salisbury has quite a good range of options for walking. I don't know much you can travel about the area but the New Forest is about a 25-30 minute drive away. It has a huge range of routes on offer. Much of it is open access land so you can follow any of the numerous tracks across it and decide on your own routes. Despite the name, not all of it is forested - in fact, much of it is open heathland. There's too many routes to list here but a quick search online should bring up a few: my favourite spots are near Bolderwood, Godshill and Beaulieu.
Closer to Salisbury, you can take a wander through the fields and forests along the Clarendon Way which would eventually take you to Winchester, but that's more than one day's walk! Around Downton there are some nice walks along the river and out through the fields.
Again, if you have access to transport you can head further north into Wiltshire and explore parts of Salisbury Plain, but much of that is limited access.
As for difficulty, it's not particularly difficult: there's the odd steep spot but much of it is gentle rolling countryside.
Hope this helps.