You're pretty safe here as long as you stay clear of the North Side and the run down areas of south side and downtown.
If you're looking at something like apartmentguide.com, you'll probably be able to find places that specify optional month to month leasing options.
Personally, I would try to do at least a three month lease, and look on richmond.craigslist.org for people who possibly want to sub-lease.
With all that said, based on your interest in music and living animal cruelty free, used/independent bookstores, yoga & etc. I suggest the Carytown or Museum District areas. The rent may be higher, but like anything else you get what you pay for. These areas are surrounded by things you are interested in, all within walking distance. The Fan, Carytown & Museum District area is a historical section of Richmond, and filled with apartments & divided row-houses that have amazing style and charm.
I believe location to be the most important factor in dwelling. If it sounds too good to be true, it is. (I know this the hard way, renting a $625/month 1 bedroom apt on W.Franklin St where the noise was the least of my problems....oh the roaches!).
Great Vegan options all over the place. Ukrops has almost anything you would want. Panda-Veg is vegan chinese & japanese cuisine with excellent prices. Sticky Rice also has great options. (Lot's of restaurants here cater to animal lovers/not eaters so you won't have any trouble adjusting).
If you live anywhere near downtown or the fan/carytown/museum you're surrounded by music. styleweekly.com is the local entertainment/art/music/food guide. The art galleries here change their exhibits often & The Virginia Museum of Fine Arts (I've been here two years, and the renovations still aren't complete), Belle/Brown Isle is great spring-fall. There's a dog park off Blvd. Yoga galore down here, all different types. Mostly reasonable pricing. Used & Ind. Bookstores on Main. Metaphysical shops
The Guardian Dragon Metaphysical Shoppe and we have a Crystal Healing, Reiki, Shaman population. Two of my friends are heavily involved with all of these, and I'd be happy to pass along their email info if you have more specific questions.
Hope some of this helps. Richmond is a great place to live & I can't say enough great things about what it has to offer.