A Nice Place to Stay
Ah, the tough part of the trip. And what makes choosing the right hotel for a 4 Kids 'n Us vacation? Just that - we have 4 kids along. Many hotels cater to couples, or families that can crunch into 300 sq. ft. of space and two beds. Sure, you could get two rooms, but that gets expensive.
Luckily, your options for traveling with family today is better (not great, but better). There has been an explosion of "all-suite" properties that have reasonable rates, and more space. Some cater to business clientele, but some have targeted those families who are traveling with little ones.
The ideal hotel (for us, anyway) needs to have at least 3 beds (or two plus a sofabed or similar arrangement), an indoor pool (at least for the non-summer months), and some type of breakfast arrangement. Let's face it - mornings can be sheer torture when you have a bunch of hungry children who need to get ready to go "out" to eat. *Gasp*. I'd rather have a root canal. Sans novacaine. In addition, we have one who's allergic to pets, so we always ask about the hotel's pet policy. Here's what we found in Burlington:
Our Experience
After checking with several of the hotels in the area, I got recommendations for several all-suite properties, including the Hawthorn Suites. Check-in was easy, and we got an upgrade for $20. The suite we had reserved had two double beds, and a sofa sleeper in the living/kitchen area. These suites adjoin a room with a king bed and another bath. Our upgrade allowed us to have the adjoining room as well, which was nice.
Living Area
Living Area #2
Living Area #3
Bedroom
Bedroom #2
Bathroom
Bathroom #2
King bedroom
King bedroom #2
King bathroom
We had the swimming pool to ourselves. 
There is also a small exercise room. In addition, our wing had it's own library, in case you didn't bring your own reading material. 
The kids thought breakfast was great, and we discovered that a cat is one of the permanent residents of the property. In fact, when I went to check out, the cat was sitting on one of the sofas in the lobby. If one of your party is allergic, best leave them in the car while you do the checking in.
I'm not sure why it was so difficult to find a hotel that didn't allow pets in Burlington. I'm sure someone will fill me in on the forum.
Other choices in the area include:
Hawthorn Suites Burlington. The Hawthorn Suites has 104 one- and two-bedroom suites. They have an indoor pool, serve a complimentary breakfast (eggs, bacon, waffles, etc.), and have a separate "no pets" wing. They also had the honor of being the most referred hotel in the area. hawthornsuitesburlington.com/
Holiday Inn Express Hotel & Suites. 84 guest rooms and 78 suites. The suite was described to me as having a king bed, a sofa sleeper, and another queen bed in the upstairs loft. They host weddings and other events, and was the second most referred hotel; however, there was extensive road construction going on right in front of the hotel the week we wanted to go. This would have been our first choice, otherwise. Holiday Inn Express
Sheraton Burlington Hotel & Conference Center. The largest and "most luxurious" hotel in Vermont, offering award winning service and accommodations. They have 309 rooms, including adjoining rooms. Not exactly family friendly, and not inexpensive either, but you can't go wrong with Sheraton. .www.sheratonburlington.com
Wyndham Burlington Hotel. 256 rooms, right on the water, and the closest to the downtown and shopping areas. They did have suites available -- the Jr. Suite featured a king bed, a queen sofabed, and they had $20 rollaways available. www.wyndhamburlington.com
Marriott Residence Inn/Towneplace Suites. Marriott has both properties just outside of Burlington to the East. The Towneplace Suites has 95 one and two bedroom suites, and the Residence Inn has 96. We have stayed at many Residence Inns throughout the country, and have always been favorably impressed. They have the best breakfast buffets, and the rooms are always well-appointed (if not luxurious). The Towneplace Suites are supposed to be as nice. However, both these properties allowed pets. Residence Inn
Towneplace Suites
