I've lived in Orlando for about 10 years in many of the various "suburbs." $700 a month might be a little though, especially with kids where you would need a bigger place. You also need to think about what schools are in that area. While downtown might be the most convienent, it will probablly be the least affordable as it is one of the pricier areas. I would also recommend looking "east-west" vs. looking "north-south" because I-4 traffic is straight up miserable. There is also lots of road work planned for I-4 in the next few years, so the situation might not get any better. Going east-west, you could take 408 to downtown with less traffic, although 408 is a toll road.
For the best schools, Seminole county might be your best bet. Someone mentioned Altamonte Springs which isn't terrible except that you will need to go down I-4 to get downtown. I'm also not sure if you would be able to find something in your price range.
Metro West could be in your price range, and the schools aren't that bad, but I have a friend that lives there and the neighborhood has had a lot of increase in crime (actually Orlando in general has had an increase in crime) over the past few years.
Directly west of downtown has the worse schools in the area and the most crime. You would need to be out in Ocoee before it gets better and that is pretty far west of downtown. You would need to take 408 to get to school.
East of downtown is nicer but pricier. You MIGHT be able to find something in Colonial town in your price range. Maybe. If you luck out, you can get in an area that goes to Winter Parks schools which are some of the best in the area.
Furhter East toward UCF you could find stuff in your price range and the schools aren't that bad. I live in the far south east corner of town and it takes me about 20 mins to get to FAMU Law area at night, and anywhere from 30-45 mins during the day depending on traffic. You could cut this down by living a little further in. The schools on the East side of Orange county aren't as good as Seminole County or Winter Park, but they are decent.
If you want you can PM me and I can give you more details.