My family and I am in the process of relocating from Chicago to Orlando with a 2.5 year old, so I understand exactly what you're going through. My company placed us in corporate housing in Baldwin Park at The Village at Baldwin Park; we are happy with things. Quite frankly, everyone pushed us to purchase in the Dr. Phillips and Windermere areas, but we fell in love with Baldwin Park, so we're taking our time to ensure that we find the right "fit."
- it's walkable
- it has a sufficient number/kinds of amenities in the Village Center, i.e., dry cleaner, grocery, salons, restaurants, gymnastics and swim school (classes for kids starting at 2 yrs.), there's also a Bright Horizon daycare in the community
- it seems safe
- it borders Winter Park, which also has extensive resources, albeit it is a more established community. Winter Park has some fantastic restaurants, including one of only two Whole Foods in the area. It also has some wonderful gardens, parks and museums (the Science Center has daily children's programs, i.e., story or music hour)
- Not close to highways
- connected to the dreaded I-4 (the commute times don't bother me, I'm a city kid)
- many people perceive BP as being overly crowded
- they are a bit underdeveloped from a retail perspective
You will probably be able to find a 3 br/2 ba place at or around $2k, but you probably won't be able to go much lower than that in the area. Check out The Village at Baldwin Park, Post Lake at Baldwin Park and Enders Place at Baldwin Park just to get a sense of market prices.