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OP the school district must provide transportation for children to their assigned school if the school is 1.5 miles from home. However, if you request reassignment to a different school the student/parents are responsible for transportation. Our state provides some of the oldest buses in the nation and thus lots of parents drive their children to school each day. This may be something to consider when looking for a specific area to settle. Elementary students are usually picked up/dropped off at their home or within a house or 2.
We moved here in 2006 and looked at a lot of the neighborhoods you listed. We choose River Reserve (back when less than 20 families lived here) and love it. It is close to downtown Greenville and you can get a bit more land etc... We really wanted a basement and 3 car garage so that really limited our options. Right now houses are selling in RR for around what we paid in 2006 to a good bit more. Prices have fallen some but since we bought before the neighborhood really took off we have not taken a hit. So I would say your budget is on target for a resale in RR, it just depends on the house since several are for sale at over $900,000. We are glad we did not wind up in Simpsonville but that is due to where my husband works, the drive from Riverwalk and Kilgore would have driven him nuts by now. I also like Collins Creek, Parkins Mill, Greenville Country Club, Augusta Road (hard to find the right size house but is possible) and Cleveland Park areas. Good luck in your search. By the way I would have the same concern about ponds we are near the river so not too much stagnant water but the mosquitos are awful in our wooded yard.