hmm - "walkable", huh? Well, that all depends on what type of stores & restaurants you're looking for. Keep in mind that Houston has NO ZONING (yep, never has & never will - comes up for a vote about once a decade). So basically, if you're more than half a mile from a mini-mart, you're probably not in Houston. Instead of zoning, we are governed by neighborhood associations (the dreaded HOAs) that can have incredible power.
MidTown & Upper Kirby are new mixed-use development areas.. both very close in, but they are both very pricey. Doubtful that you'd be able to find anything in your preferred price range. I encourage you to check out the fringes of River Oaks... There are some older complexes in the Shephard/West Gray area. Great shopping along West Gray, as well as the great West Gray Landmark theater and the legendary dueling Starbucks right across the street from one another. This area is much more quirky than the newer 'perfectly planned' areas - frankly, those give me the willies. There are also quite a few big old fourplexes along West Gray. Another nice area is the Westheimer/Montrose neighborhood. You can drive down Montrose directly to The Medical Center, so it's not a bad drive.
Another really cool area just north of I-10 is The Heights - lots of character but it has been 'discovered, so prices are going up. It's a bit further away, but not a bad commute. You may also want to take a look at the complexes along Washington avenue (between I-10 and West Gray). There are several parks, nice eateries, and live entertainment in that area. Commute to the medical center from either of these areas via Shephard.
So, now lets talk about the whole 'walking' bit. You will discover that H-town is Africa-hot for quite a few months... temp & humidity both in the high 90's. If you are into outdoor exercise, you will need to avoid the hours of 10am-4pm during a large part of the year. Walking more than a block or so can become a test of endurance. Frankly, that's why the entire downtown area is honeycombed with air conditioned tunnels... and why there are basically no pedestrians on the surface. We natives don't try to fight Mother Nature, especially when the concrete resembles the surface of the sun. Walking is just not a Houston 'thing'.
But, never fear - we do have 4 seasons: Almost Summer, Summer, Still Summer & Christmas. I hope you love Houston as much as I do!