A very, very simple compromise solution: Each degree latitude equals 111.11 km distance. If you are looking for places x miles apart, the difference in latitude must be less than x * (1.609 / 111.11). So if you start at (LAT, LONG) then all users must have LAT - x * (1.609 / 111.11) <= lat <= LAT + x * (1.609 / 111.11). Use that for a query to MySQL; if you are looking for a distance of 50 miles you will filter out a lot of candidates.
There are better, but more complicated solutions.
You don't need MapKit. Calculating the exact distance is very complicated, but for small distances and not very much precision there's a simple method.
Each degree latitude is 111.111 km. Each degree longitude is 111.111 * cos (latitude) km, where the angle of the cosine is taken in degrees. The distance from (LAT, LONG) to (lat, long) is approximately
sqrt ((LAT - lat)^2 + ((LONG - long) * cos (LAT))^2)