Hard to say a best, though I'm sure you'll get many people claiming one or the other to be so, "hands down" no doubt.
Some good ones:
Hodad's in OB - Basic burger, but with a generous amount of toppings, and they have an unusual form of bacon on the burgers.
Rocky's in PB - These have a lot of devotees. They are good, though nothing beyond burger w/ cheese in terms of options.
Crest Cafe in Hillcrest - Tasty, and they will cook to order. Some interesting options, good bread.
Phil's BBQ in Sports Arena - They grind their own chuck, and cook the burger over open flame. One of my favorites in town, though I get sauce on the side.
The Linkery in North Park - Probably the biggest burger. Topped w/ bacon, pineapple, grilled onion, and a fried egg. One of the best.
Cafe 910 in La Jolla - My favorite in SD. They'll cook it rare and serve it on brioche. Perfect in every way.
Sammy's - They have mini Kobe beef sliders on sweet Hawaiian egg bread. They are very delicious, if atypical. Another of my favorites.
Liars' Club in Mission Beach - Lots of cool variations, all of which are worthwhile. Great beer selection, too.
For cheapest options w/ college students, I'd suggest Hodad's, Phil's BBQ, Liars' Club, or Crest Cafe for two reasons. One, good burgers. Two, they serve good beer.
Rocky's gets major demerits in the beer department. They only serve crappy macrobrews, with the exception of Widmer Hefeweizen, and that's not so great either: still Rocky's is cheap, burgers there are around $6. The wait can be insane. When I went, on a Sunday around 1pm, it was standing room only, and took an hour to get my burger. When I finally got it, I kind of wondered what all the fuss was about. I sometimes wonder if their fans have ever ventured beyond PB to see what else is available.
Burgers at Hodad's can be as cheap as $6 for a combo w/ fries if you get the mini size (which is actually what I order when I go). The mini is 1/4 lb. and if you get it w/ bacon and cheese is quite satisfying. They don't put the mini bacon cheese on the menu, but you can order it. They have a few draft beers, including some local options.
Phil's BBQ burger is $6 and is 1/2 lb. They have a nice choice of sides that are $1.50 apiece. Their beer selection is a little better than Hodad's, IMO, with some very good local handles/bottles available.
Liars' Club is another good deal, burgers are $7 and come w/ fries or cole slaw. You can see a list of their burger options at their website, http://www.liarsclubsd.com - I particularly like the Fuego Burger and the Jerk Burger. Beer selection is the best of those listed, with a huge number of local options.
Crest Cafe is a little bit more expensive than these places, with the 1/2 lb. burgers starting at $7 for the plain option, and hovering between $8 and $9 for the specialty choices. They have some interesting sides, the jicama cole slaw is quite nice.
If you're interested in eating late at night, then Liars' Club and Crest Cafe are your best bets, as they are open until midnight.
Rocky's!!! I used to live in PB, just a couple of streets from there, so I would go once every couple of weeks to get my red meat fix. Oh my gosh, I love their burgers. Now I'm clear across the country and when I go back to visit friends, I still make them take me to Rocky's!
Here are my favorites (in no particular order)
The Vine: I don't really know why this burger is so good, but it is. They use a wonderful ciabatta -like roll, and use excellent cheese. More Artisan than most of the places you will find on this list.
Tiolis Crazy Burger: A relatively new place to the game, but darn good. They have some 27 variations of burgers - including Gator and Rattlesnake. I personally prefer the Dansk, which is a simple burger with lots of bleu cheese on top. Darn good french fries too.
Hodads: Simple, but still a favorite.
The Linkery: Not your traditional burger. Some people can't get beyond the fact that there is an egg and a slice of pineapple on their burger, but I happen to like it.
Liars Club: Really not known for their burgers, (I order the fuego steak melt 99 % of the time) but pretty good. Go for the beer, but enjoy the hamburgers.
I like Tiolis Crazy Burger on 30th. Great choices of burgers and (I guess most Americans are not interested but for me it is important) German soccer television.
HeeHee, the Longhorn has been around for a V-E-R-Y long time and turning out pretty decent burgers. There is a photo in my high school year book (Senior year) of some of the members of the football team at Longhorns chowing down. Let's see...that would have been Patrick Henry, 19....oh my god that was a long time ago...