Edit 2:

Now for a more serious attempt at something efficient..

findPoints = Compile[{{n, _Integer}, {low, _Real}, {high, _Real}, {minD, _Real}}, Block[{data = RandomReal[{low, high}, {1, 2}], k = 1, rv, temp}, While[k < n, rv = RandomReal[{low, high}, 2]; temp = Transpose[Transpose[data] - rv]; If[Min[Sqrt[(#.#)] & /@ temp] > minD, data = Join[data, {rv}]; k++; ]; ]; data ] ]; 

And to test it for benchmarking...

npts = 350; minD = 3; low = 0; high = 100; AbsoluteTiming[pts = findPoints[npts, low, high, minD];] ==> {0.0312004, Null} 

Check that the min distance is less than the threshold.

Min[ MapThread[ EuclideanDistance, {pts, Nearest[pts][#, 2][[-1]] & /@ pts}]] > minD ==> True 

Check that I generated the correct number of points..

Length[pts] == npts ==> True 

This is not an efficient answer but it is fun to play with so I thought I'd post it. For efficiency the use of Nearest might provide a good starting point.

g[n_, {low_, high_}, minDist_, step_: 1] := Block[{data = RandomReal[{low, high}, {n, 2}], temp, happy, sdata, hdata}, While[True, temp = ((Nearest[data][#, 2][[-1]] & /@ data)); happy = Boole@Thread[MapThread[EuclideanDistance, {temp, data}] > minDist]; hdata = Pick[data, happy, 1]; sdata = Pick[data, happy, 0]; If[sdata === {}, Break[]]; sdata += RandomReal[{-step, step}, {Length[sdata], 2}]; data = Join[sdata, hdata]; ]; data ] 

The idea is to do an initial sampling and then allow the points that are too close to "walk" somewhere else. The function takes a desired number of points n, a low and high value for the data range, the minimum acceptable distance between points minDist and a step argument which allows points to "walk" up to a certain distance in the x and y directions.

Its especially fun to watch dynamically.

g[150, {0, 30}, 1.5, 1] 

This is not an efficient answer but it is fun to play with so I thought I'd post it. For efficiency the use of Nearest might provide a good starting point.

g[n_, {low_, high_}, minDist_, step_: 1] := Block[{data = RandomReal[{low, high}, {n, 2}], temp, happy, sdata, hdata}, While[True, temp = ((Nearest[data][#, 2][[-1]] & /@ data)); happy = Boole@Thread[MapThread[EuclideanDistance, {temp, data}] > minDist]; hdata = Pick[data, happy, 1]; sdata = Pick[data, happy, 0]; If[sdata === {}, Break[]]; sdata += RandomReal[{-step, step}, {Length[sdata], 2}]; data = Join[sdata, hdata]; ]; data ] 

The idea is to do an initial sampling and then allow the points that are too close to "walk" somewhere else. The function takes a desired number of points n, a low and high value for the data range, the minimum acceptable distance between points minDist and a step argument which allows points to "walk" up to a certain distance in the x and y directions.

Its especially fun to watch dynamically.

g[150, {0, 30}, 1.5, 1] 

Edit: Per suggestion of Yves Klett the points are colored by relative happiness (green being more happy, red being less happy).