I stayed at the Rose and Crown on Rick's Southern England tour. It was a good location, easy to walk to the city center and nicely sited on the river. We were there on a Friday and Saturday night and apparently this is/was a big venue for weddings and celebrations. My room faced the garden area where these are held and it was pretty loud until midnight including a disco ball, haha. IF you aren't going on a Friday/Saturday I'd have no qualms about staying here again. The breakfast was fantastic...but it was pre-covid so not sure if they still have their fabulous breakfast buffet.
I've also stayed at the Mercure White Hart on a Road Scholar tour. It was really well located (just a block or so from Cathedral View) but was not as nice on the inside as the Rose and Crown. This was in 2016 and it badly needed updating. Breakfast was so-so. I'd probably only stay here if every other place was booked.
I've also got my eye on the Best Western Red Lion. I've walked back into their courtyard on a walking tour of Salisbury (from the Tourist Information office) and it is pretty cool. It's got some 13th Century parts still in use as I understood it. I've not stayed there but am looking at it for my next stay in Salisbury.
https://the-redlion.co.uk/history/
Are you going to have a car? Rose and Crown might be easier for that as I think they have some parking and it is a little away from the City Center. You'd have to check. The other 2 are right in the city center and might have more difficult parking access. I do not know this for sure as I have not driven in England.