Hi Wendy,
Welcome to the Lake and the Forum. You've had some very good advice here so far. Almost all have suggested a lake chart/map.
Let me suggest that you get the Bizer map/chart rather than the "green" map by Duncan Press. The omissions on the latest Duncan Press (2005) edition and their failure to make timely corrections to the information on their web site could be detrimental to your boating experience. For instance, they STILL list only TWO areas of the 45/25 mph speed limits on the lake. The limits apply to the WHOLE Lake, not just the two areas Duncan specifies.
You can see more inaccuracies of the Duncan Press information in
THIS POST and the associated thread.
They haven't changed the information since that was posted July of 2009!
Others have mentioned anchoring in shallow sandy areas and swimming, usually they are favorite spots that eventually get designated as "NO RAFTING ZONES" or NRZs. The NRZ is a misnomer as rafting is tying two or more boats together while the NRZ restricts rafts to no more than two boats and includes other restrictions such as anchoring distance from shore, other boats and boat rafts. Duncan Press (Green map) omits several NRZs from their map and web site. Check Bizer's map and their web site
HERE and click on corrections to have the most accurate list and location of NRZs. They are the best shallow sandy spots to anchor and swim. When doing that it is advisable to use TWO anchors to keep your boat from moving around too much. One off the bow and another from the stern.
Do NOT rely on the Duncan Press corrections web page for the most accurate information (as of this date)
The place near the Governor Island Bridge that was mentioned for anchoring is a NRZ and the Marine Patrol has been enforcing the anchoring distance rules there more often the last few years. I believe it is 150' from shore while other NRZs, like Braun Bay has anchoring only 75' from shore.
Depending on where your slip is at MVYC backing the boat in can be a bit tricky particularly with some wind. As mentioned earlier, tossing a float out in open water and backing to it is good practice. When going to your slip don't be afraid to ask for help - those on shore will be glad to assist you in getting in.
My last bit of advice is about markers. There are some places where the best route is not intuitive - so always check your chart/map. Did we mention it is convenient to have a Marine VHF Radio on board? Boaters usually monitor Channel 16.
I've been at MVYC for about 15 years. I'm sure you'll have many happy times at the Lake and at MVYC. Happy and Safe boating