New Hampshire is an excellent place to look for Moose. There are bus tours you can take, but instead I recommend you do what I did and take a road trip to Pittsburg, NH. Route 3 from Pittsburg north to the border is an excellent stretch of road to find moose in late evening or very early morning. I would recommend morning as it's easier to get clear photos. Be careful driving the road at all times they are active at night and harder to see. Deer are also frequently in the roads in New Hampshire, keep your eyes on the road at all times. If you only wish to see moose a single day is long enough but there are many excellent hikes and paddling adventures in the area, so three or more days would be ideal. There are many cabins, lodges, and motels in the area to choose from, but if you don't mind camping, I would recommend Deer Mountain Campground located along route 3 just miles from the border. Keep in mind it gets cold at night in the area even when it is warm during the day, so bring warm clothes and a blanket. When I stayed in June it went down to 45F at night.
Besides Moose, loons, grouse, fox, turkey, deer, and black bear were seen.
The Connecticut lakes are scenic and good for fishing or larger boats, for non-motorized paddling I would suggest the quiet streams and lakes that can be found at Scott's Bog or elsewhere on East Islet road (many choices). For Scott's bog, turn left off East Islet road, stay left until you see the boat sign and turn left again.
Or stay right on East Islet road and you'll find streams and lakes such as this one, along with hawks and grouse along the road. Be careful, several miles onto East Islet road is a low dip with rocks poking up. Go slow, especially if you're in a low clearance vehicle and not used to driving on rocky, dirt roads. The first few miles are fine for any vehicle, but again go slow as the grouse run out onto the roads.
Finally, let's talk about those Connecticut lakes. The first is closest to town and fairly large. The second appears to be smaller and less visited. The third is just a mile or so from the border.
Visiting the fourth Connecticut lake requires parking at the border (there is a sign). You will then walk behind a fence and cross the road to the left. The trail is clearly marked so you shouldn't have any issues finding it but stay on the trail and don't veer off as you're walking right along the border. This is the headwater of the Connecticut River which later becomes a massive river. I attached a picture of the Connecticut River as it is by Deer Mountain Campground and you can see it's still quite small at that point. The trail climbs for a short distance giving views into Canada.