Since you do not have requirements for projections and mappings, you could use flat-earth approximation which converts decimal degrees to nautical miles. From there you can convert to feet, meters, etc.

Flat-earth approximation is really quite simple. There are 60nm per degree. So
y = latitude * 60;
x = longitude * 60 / cos (latitude);

This is fast and light weight. If you really want to localize and minimize errors, you can also subtract a local reference latitude/longitude for the park or area in question. For more robust map projections, I use GDAL (gdal.org) and PROJ.4 (proj4.org). This allows me to position anywhere in the world with surveyor accuracy. It is not as light weight but it is robust and well supported. GeographicLib also has great API for UTM/UPS and MGRS conversion.

One problem you could have with tight points and scaling is that if you do NOT use line width 0 in your pen, the pen width will scale as you zoom. I typically make my point diameters 1ft or .3048m and this tends to make zooming better.

Zoom in closer on the area in your view?

Otherwise, what behavior would you like to see if the points overlap?

Do you have any solution for this?

In your case, the distances are so small, that you can use a quite simple one. Perhaps a simple "equirectangular projection":http://en.wikipedia.org/wiki/Equirectangular_projection will do fine for your purpose.

You can use the formula in the article referenced above to get a set of x, y coordinates. Then, all you need to do is to scale and transpose these coordinates so they can be mapped in a sensible way to your screen.