Stephen, Generally, between late April to late September, hey, ha.
Kidding, but not by much. There are several bad hatches that happen up there and really difficult to say exactly when. A few degrees may mean a couple, three weeks.
Blackflies: Usually 2-3 weeks each side of mid-May to 2-3 weeks each side of the end of June. They MUST have bare skin to chew through. They can happen most anytimee in some areas, soo, count on very few most of the 3 season camping time. DEET slows them down since they will crawl around looking for a sweat gland to chew on. They like IR, ie warm things.
Mosquitoes: Pick up about mid-June and remain till cooler weather in late August. However, the first batch in spring are voracious often ignoring DEET. They can bite through a single layer, sometimes two layes of clothing. Some areas have a LOT, some areas have none. They like CO2.
Deerflies: Usually these are the hotter months. I have had CLOUDS of them attack me between July 15 and August 15. Wear a hat since they like high moving objects. DEET does not work on these. They like moving things.
Tic's, biting midges, no-see-ums, etc. These can crop up anytime. Mostly during July and August. But, I have had no-see-ums in late September.
Fleas: Sand fleas on the beaches in warmer months. They can get into your bag making it miserable for a couple weeks. Same for bed bugs, but these are usually found in forested/warmer areas.
Spiders, chiggers, etc. Usually not in early spring or late fall, but it has happened to me. I will get a line of bites along a leg…3,4 or 5 bites that itch like h#ll.
Latter September can have a minor black fly hatch. Minor I say…well, if you happen to be there, they are just as miserable as spring for a day or two.
Permethrin on clothing, DEET on skin as needed, seems to build up over two or three days, but washes off easily. Some evidence that 3-4 days unshowered helps, or, do not use soap of any kind. Plain water rinses help a lot with smelling but does NOT draw bugs. Dr Bonners seems to work as poorly as any other. Picarden helps for short term use. Some others also work short term. Smoke deters them all. Smokey campfires, pipes, cigars, or, cigarettes are good for detering them around your head. Tipped cigars are common but a source of messy trash. Using all these methodes I can usually head out comfortably anywhere the ADK's. Movement will help, keep on a'truckin' as they say.
The ADK's are not only the high peaks areas. Though people not living near there seem to concentrate in that area. This only comprises about 1/6-1/8 of the state park. Lots of hills, lots of water and swamps, lots of bear and other critters lots of hiking & paddling.
http://alavigne.net/Outdoors/FeatureReports/Adirondacks/index.jsp?navpage=overview
http://en.wikipedia.org/wiki/Adirondack_Park