I am not exactly sure what you mean by ''cruising down the East Coast''. That could mean a lot of things (a cruise from Maine to Key West or simply cruising on the Atlantic coast) that could affect the type of boat that you works for your needs.
With a wife, two kids and a dog I would think that you would minimally need around a 30 footer for simply weekended in and perhaps a week of point to point cruising. (Without the dog you might get by with a 25 footer but that''s another story.)If you literally mean a cruise down the East Coast then you are living aboard and cruising and that suggests a boat over about 35 feet with 38 or so feet being more ideal.
If you are literally, ''doing the ditch'' then draft under 6 feet is helpful. It is nice to have a boat that is laid out so that there is enough storage so that the bunks can be left made up and enough water to support 4 people and a dog for a 5 days or so incase you want to jump off at the Keys and come in at Hatteras. With a $40,000 budget I would try to keep the boat simple.
One more point, cruising boats of this size and in this price range are going to be older and more tired than either a more expensive or smaller boat. You will be looking for an example of an older boat that has been taken care of, updated and is in good shape. You will see some that have really been trashed. Take your time and make sure that you have a NAMS or SAMS certified Marine Surveyor survey what ever you buy.
Here is a list of possible suspects:
Allied Princess: Slow, solid, simple boats that were well built but not exactly elegant down below. It would not be my choice but they are certainly a workable boat for what you want to do.
Cal 36: Venerable and beautiful boats. They sail well and offer a lot of boat for the money.
-Chris Craft Apache 37: Most people don''t remeber that Chris Craft once built a line of quality sailboats. The Apache was a very nice boat for its day. They sailed well and had a simply but close to ideal layout.
-Columbia 38: These are classic mid 1960''s era cruising boats. They were built as both centerboard and deeper keel versions. They will be comparable slow and cramped for their length but are good boats. They should not be cinfused with a Columbia 39 or 40 which I advise against.
C&C 35: Good all around boats. Quite cramped by modern standards and probably too small for distance cruising but a good boat for weekending or short point to point cruising.
-C&C 38: A more modern design than the 39 and offers a bit more room. A little short on fuel and water tank capacity but that can be added. There were several versions including a centerboard version. This is not the same boat as a C&C Landfall 38. The Landfall 38 never did anything for me but a landfall 38 might workl for what you''d like to do if you found one in your price range.
-C&C 39: Good older design. Well consturcted and quite fast. Their easily driven hulls mean that you can get by with less sail area. Nice workable layout but quite tight for a 39 footer. A little deep as well.
Hunter 37 cutter: Hunters take a lot of criticism on the internet. Some of this criticism is fair, a lot is not. In the early 1980''s Hunter built a number of pretty heavily built boats that were good all around boats for the kind of thing you are considering. These included the Hunter 37 cutter and the sloop rigged version of the same boat, the Hunter 36. They had nice clever layouts and good sailing characteristics. That said you need to find an example in good shape as many of these have been really trashed over the years.
Hunter 40: This is a more controversial choice. I have always liked these boats. They sail well and have a very nice interior layout. They have a very workable deck plan. BUT they were not as well built as some of the boats on this list. Again, you are looking for one that has not been beat to death.
Morgan 382 (38): These Ted Brewer design are nice well rounded designs that sail reasonably well. They are not especially fast nor are they good in light air but they are considered to be good sailing boats. (BTW There is a 38 foot Morgan Out Island that is for sale at Light House Point that is mislabled as a Morgan 382 in the listings. I am not a fan of the Out Island series but they sure seem to have their followers)
-Newport 41: This is a big. pretty, inexpensive boat. Simply constructed and not the sturdiest boat in the world, they are very good sailors and offer a lot of boat for the dollar. With a 6''3" draft these will be trickier boats on the ICW but will offer reasonably good light air performance if you end up sailing Long Island Sound or the Chesapeake.
Niagara 35: Solid, go anywhere, cruising boats.
Pearson 35, 36, 37: These are three very different boats. They are probably too small for distance cruising with your gang but a good boat for weekending or short point to point cruising.
-Pearson Invicta: Not the most common boat out there, the Invictas are centerboard yawls and sloops from the mid 1960''s. They are good sailing boats with a reasonably nice, but simple interior layout. They are a dated design in many, many ways but they are good sturdy boats.
-Ranger 37: A lot of these old race boats have been fitted out with nice interiors and offer a lot of boat for the money.
Rhodes 41, Rhodes Bounty: Venerable older boats. You should find one in really nice shape for less than $40K but it may still have a gas engine and a fair amount of work. These are good boats for a lot of things but you do give up some performance and some ability in a chop with these old girls.
That''s a quick list. I need to get to the office.