Trains from Salisbury to London (Waterloo station) run every 30 mins most of the time, and take about 1.5 hours for the journey. The railway station is on the edge of the city, but as it's such a small place that's only about 15 mins walk from, say, the Red Lion.
I think it's a perfectly good idea. I know people who commute from Salisbury to London for work, and if they can do that (including going out for a drink or meal in London after work), I'm sure it's fine for a day trip. My mother still lives just outside Salisbury, and she sometimes comes up to London by train for us to have a day out together.
Do check before travelling at a weekend whether there are planned engineering works - it can take the gloss off a nice day out to have to change to bus for Basingstoke to Woking strecth, or similar. They do only affect about 1 weekend in 5.
If there are no engineering works at the weekend, it's good to know that you can upgrade to first class for an extra £5 each way - you just sit in first class with your standard class ticket, and tell the ticket inspector you want to pay the extra £5 for the upgrade. Only at weekends though - during the week you can only travel in first class if you have bought a first class ticket before you get on (or they expect you to leave your firstborn, or two limbs, in payment). For me, first class isn't worth it at the weekday rates, but I always do it for my fortnightly Saturday journeys back from my mother.