Breezer is a brand. Uptown is an entry in their line of bicycles. "Infinity" means it has the Nuvinci non-gear gears:
About ten years ago, R. and I went to the Netherlands. I had been telling him I wanted a bike like that, and he thought they weren't available in the US. And by "like that", I meant internal gears, upright riding position, stepthrough frame. I found three bikes: Bianchi's Cafe Racer (which was my present that year), the Electra Townie (which I bought a few years ago) and some Breezers. The Electras and the Breezers were only available with the Shimano Nexus 3 speed -- the Cafe Racer had the 7 or 8 speed (I always forget), so that's what I got. When the Townie had the better gears, I got one. Later on, the Nuvinci happened and I've been trying to buy a bike with that ever since -- but it still had to satisfy my other criteria.
The Uptown has an upright riding position, however, it is not crank forward a la Electra. So, bummer there, but of course R. loathes the Townie so he's happier on balance. The step through is deep, and the bike itself is light and stiff, which is quite nice from both our perspectives (the Townie is too heavy to comfortably lift on top of the car). The Uptown comes standard with a dynamo and light (they run the wire through the fender and included rack, so if you intend to swap accessories, think long and hard). The seat is decent, but not a Brooks saddle. The rack is perfectly adequate, altho not a Moose Rack, so I won't be towing the Burley Kazoo, altho I may be able to haul the WeeGo. They included a bell AND a wheel lock in the rear, however, the frame lock does not integrate with a chain. Basically, it's what we're used to when someone tricks something out for us: they compromised on everything -- but the price was a lot lower than what it would have cost to produce the equivalent (and believe me when I say, I _know_ what's involved in getting a dynamo, light, etc. on a bike).
The Nuvinci is a dream. You cannot turn the shifter arbitrarily while stopped, a la the internal gears I am accustomed to, but there is some play. It is completely intuitive but has a very cute little indicator.
It'll be interesting to see how it holds up over time, but right at the moment, I am completely in love with my new bike, which is what is supposed to happen when you get a new bike. If gears annoy you, I highly recommend getting something with the Nuvinci -- it's even better than the Shimano Nexus (boy, I never thought I'd be writing that).