If you're still looking I have some. Thanks.

I believe the situation in zone 5 is that the colder temperatures kill the plant back to the ground each year. Therefore, you only get new growth each year (kind of like a large shrub). Therefore it is likely that they won't flower for you (a good reason for the invasiveness not being an issue, eh?). If you like the effect of the large leaves (which some people do), Northern Catalpa might give you the same effect but it survives the winter and eventually blooms.

Paulownia tomentosa, or empress tree, is a very week-wooded tree that is also an aggressive self-seeder in MA, CT, and RI. Depending on where you live in NH, volunteers may or may not be a problem. It may also be winter-killed and not grow into tree form - the specifics of your locale will make all the difference. It's the only blue-flowered tree I can think of - but there are rose of sharon and tree wisteria that would not get as big and might or might not work for you. You might also call around about the tree lilac, they're pretty common. There are search engines that will show all the nurseries in your area - try http://www.gardenguides.com/resources/nurseries/ and type in your zip code. Here is a link that might be useful: USDA profile for paulownia

Don't plant a Magnolia if you're worried about mess. Someone planted one 50 years ago next to our pool. It is absolutely beautiful and give great shade to the south side of the house, BUT it is very, very messy. The large leaves drop all year, heaviest in the spring, and they take years to decompose. In the summer the beautiful flowers drop bud sheaths and then petals. Later in fall, heavy cones drop and bring tons of squirrels who pull them apart after the seeds and leave a mess everywhere. Plus the cones are kinda spiky, painful if you accidentally step on one, plus a tripping hazard. So yes, a beautiful majestic tree...for the outer edges of a property, not near a patio. You have been warned, lol. The Africarpus gracilior is a pretty good choice, they do get huge with age, but are fast and pretty clean, and handle heat and soil compaction well. Josue Diaz's suggestion of Brachychiton populneus is a good choice too, lovely tree, too tender for where I am, but should do great for you. Stan's suggestion of a Tristaniopsis laurina is a good one too, but pretty slow growing. If you want shade soon, I'd get the largest one you can find. It will be expensive, but save you several years waiting. I love Ficus microcarpa (Indian Laurel)! Beautiful tree, gorgeous white smooth trunk! I just got back from visiting my daughter in San Luis Obispo and the downtown streets are lined with them and they're very majestic. Do be aware that they can get very large buttress roots with age, but if you give them lots of root room near the patio, but not right next to or in the patio, they should be fine.