Another vote for Pondicheri's.
Also in that area, I have been to Radical Eats which doesn't fall into your price range but their Sunday brunch is very good and AYCE. Whole Foods salad bar is an option. Also, Trader Joe's is nearby and they have cheaper options, too.
There is also a Greek resto, Niko Niko, near Montrose/Westheimer but I have not been.
Not close, but my latest find has been The Dosa Factory. Right now, a free appy with every dosa. Each dosa is $7-8 with many different fillings. Free AYCE sambhar, too. There sambhar is good because it isn't uber spicy and more flavourful.
I don't know about exclusively vegetarian, but I will list a few vegetarian dishes that I love from a few restaurants that also serve meat. I, myself, am not a vegetarian so my knowledge on the subject isn't that expansive. Regardless, here are my favorites:
1. Beaver nut burger from Beaver's -- I like it more than beef; I add a fried egg to mine (it's $12, but you could probably have them take off the homemade chips for a cheaper price) their watermelon salad is also really good
2. Truffled egg sandwich from Local Foods (comes with 2 sides, I recommend the beet salad, bests beets I've ever had) all for $9.50
3. Portabella sandwich from Bowl Cafe ($7.50)
That's all I can think of for now.
Way more vegetarian options here than Austin...not in Montrose, but there are huge swaths of vegetarian indian and middle eastern places out by Hillcroft. As noted before, just near Montrose you have Aladdin, Radical Eats, Indika (cheap for lunch), Field of Greens, Hobbit Cafe, Bowl, Green Seed, Cafe TH (vegetarian and vegan vietnamese...say that three times fast), Doshi House, Baba Yega, House of Te, Jus Mac (build your own), Mission Burrito, well...that's just off the top of my head. But it should get you started...