Much of the better public transit is closer into town. Light rail is coming along (finally) and there is a great bus system. Shopping, dining/entertainment, etc are all over the place. This is a link to a PDF that shows Metro's system http://www.ridemetro.org/SchedulesMaps/SystemMaps/pdfs/METRO
Trulia as a crime feature here. You can also visit these two web sites (city and county) to review crime across the city. No place is crime free and you want to compare to where you live now.
You might want to try web sites like http://www.ZipSkinny.com to compare zip codes here to those in San Jose. Much will depend on your price range and what type of property your hoping to find. I would think your dollar will go farther here, but closer in locations are a bit pricier than the suburbs. Let us know if we can help.
Bernstein Realty, Inc.
My suggestion is the Galleria area. If you're planning to lease, you can rent a one-bedroom condominium unit for $750 to $1200 or so, depending on amenities. Most are older (built in the 1970's), but some have been very nicely updated. A single-family home (if any are available) would run closer to $2000, and most aren't all that close to the bus stops. I wouldn't recommend a townhouse, given your mobility issue. You might want to get in touch with a locating service (just Google "Apartment Locators Houston ... there are dozens of them) and let them know of your issues and concerns.
I trust that this has helped. Feel free to get in touch if you need additional information.