I haven't lived there for eight years so I don't know how current any of my recs would be. However, I'd second going to Hotel Del for Sunday brunch if you're feeling particularly extravagant.
If you're into theatre at all, seeing a play at the Old Globe in Balboa Park is pretty cool.
I've really never been into eating in Old Town (I like going to one of the many hole-in-the-wall Mexican food places around town), but I really don't know that part of SD very well. I wouldn't go for a California burrito unless you like french fries as the added ingredient is french fries. I prefer the Arizona burrito (and miss them as I've yet to find anyone in NorCal that makes them). Think California burrito but instead of french fries, it has homestyle potatoes. The one place I used to get them is in North County in Oceanside off 76 (I think at an Alberto's). One of my favorite things about getting Mexican food in SD (and in the similar places in NorCal) is that they don't fill their burritos with rice and beans (sadly, that's what often makes the burritos so huge in LA). Unless you want to fill up on rice and beans, beware that those giant burritos are likely full of them. I love rice and beans; I just don't want them in my burrito. I think you can't go wrong going to one of the 'berto's (ROberto's, ALberto's, ERIberto's and so on).
I wouldn't quite say avoid North County but just know that traffic on I-5 in either direction as you get closer to Del Mar is going to be bad due to the fair.
I might recommend going to Julian, but I've never been there. It's supposed to a great place to go for pies and is supposed to be quite scenic. However, I recall my college history professor railing about how inaccurate is the supposed historic tour for one particular part of Julian. I don't remember what, and this was ten years ago so it might've gotten better.
If you want to go to a cool coffeehouse, try one of the locations for the Living Room.
Also, if you'd like to try an cool dessert place, Extraordinary Desserts is lovely (not the one in Little Italy, but the original one).
I'd also recommend going to Little Italy if you want Italian food, although I don't remember the name of the one restaurant I've gone to in that area. I know it's on the east side of the street and near an art store and an Italian deli. However, given Little Italy is only about 2-3 blocks long and there are several Italian restaurants there, I don't know how helpful that is. I remember there's a seating area in the back that's a little elevated (there are a few steps to reach it and a rail around that area). I just remember going there years ago and having osso buco that was wonderful.
ETA -- I'm pretty sure the Italian restaurant I went to was Mimmo's Italian Village as it's next door to the pizza place. The Extraordinary Desserts location I recommended is near Balboa Park (and, apparently in the years since I've been there, has been featured on the Food Network).
The Living Room, http://www.livingroomusa.com/
-- neat local coffeehouse chain; they have them all over SD as far north as La Jolla
Extraordinary Desserts, http://www.extraordinarydesserts.com/
-- have the most amazing looking desserts I'd ever seen; it used to be standard that they'd put fresh flower decorations on their cakes but they now charge extra for them; I like the location near Balboa Park better than the one in Little Italy
Mimmo's Italian Village, http://www.mimmos.biz/
Hotel del Coronado Sunday Brunch, http://hoteldel.com/restaurant-coronado/crown-room/
-- loved their brunch but, when I went, I thought it was expensive at $40-45; it's now $85.
Alberto's, Oceanside (on Frazee), http://www.yelp.com/biz/albertos-oceanside?sort_by=date_desc
-- I can't really recommend this particular location since the recent Yelp reviews don't look very good and I haven't been there in about eight years so it sounds like they've gone downhill; however, I still recommend getting an Arizona burrito somewhere over a California burrito.