The Lawrence is very good and that area of side streets has a lot of decent pubs. A bit further along the main road to The Sir Loin of Beef but it is a great pub, quirky, full of odd junk and usually has at least 4 decent ales on. The Phoenix is also very good. The Leopold Tavern used to be fantastic (nine non-mainstream cask ales) but the Pubco did the usual and priced the landlord out and I believe it is rather ordinary now but does have tellies for live sport.
Wouldn't recommend the spoons near Fratton Park (John Jacques) before the game, will have door staff, probably rammed with home fans.
I can recommend The Lawrence. 50 yards from my house!
I have been in touch with someone who supports Portsmouth, although he doesn't live in the area now, and similar to posts from SW and Birkonian, he recommends the Lawrence Arms (though not Numbet 23's house
), the Phoenix and the Sir Loin of Beef, which are all a "brisk 15 minute walk" from the ground.
The Artillery Arms is near the away end, as is the Staggeringly Good Brewery, but both are small and liable to get packed.
If you are on the coach, and just want a beer near the ground, he suggests the Rutland Arms, though you would be drinking from plastic glasses.