Mary,
I have only done over night stays on the Hudson tied up in a slip at a Marina. We keep our boat old Tartan 27, which sounds pretty similar to your Bristol 26 (nice boat by the way), on a mooring at Nyack, NY.
You highlighted one of the reasons we generally do not anchor out overnight which is the reversing current in the river. There are also not many appropriate bays in our section of the River except by Croton Point which forms a kind of a protective area from the current and is popular with motor boats and cruising sailboats alike in the summer. It looks like Cold Spring may offer similar protection for you.
There are many on this forum with more anchoring experience then me but will offer what limited insight I may be able to shed on the subject.
1) It is good to have 2 anchors. Some people use one anchor for the bow and another for the stern. This can stop the boat from 'sailing' at anchor which can be annoying while trying to sleep. Other folks form a bridle out of both anchors (one up river (up current) and the other down river) so at least one anchor will hold when the current changes. I have no experience in this and will let others comment as to its ease of setting up and effectiveness. There is a lot of info on the web and various blogs about anchoring techniques.
2) Keep an anchor watch. Know when the current will start to change direction. If it is at all similar to our part of the river it happens pretty quickly. Here is a tide table for Kingston:
Tide Tables
Keep in mind that the time of high tide is not when the current begins to flow back down the river. There can be a significant delay between high tide and the beginning of the ebb current. It would be nice to have your 2nd anchor handy if you discover that your primary anchor is dragging in the middle of the night.
3) stay out of the channel that the tugs, barges and commercial traffic use.
4) have an anchor light visible to other boaters on deck
5) tugs use VHF ch. 13 to talk to each other
6) have a blast. Sounds like fun.