First I'll say I have asthma and allergies, and this past summer was awful. But on the other hand, every summer here has been different. The previous 2 I never had to use my inhaler. I am not sure where to find any info, but you might want to look at allergy info for this area.
That being said, I'd totally recommend Rochester otherwise. I'm not sure how the pay is as far as benefits and rates but there are definitely more jobs than just the health field. Mayo employs over 30,000 people in Rochester but there are also over 100,000 people here. So we don't all work there.

There are a lot of restaurants and hotels with restaurants - upscale and otherwise - so I would think there are chef positions available. There are several construction companies here that I can think of - whether or not they are hiring I do not know. There are definitely jobs here. Rochester is the fastest growing city in the state and I believe it shows. I did not grow up here but lived here for a couple years several years ago. When we moved back, it was amazing how much the city had changed. Since we have moved back - nearly 3 years now - a 2nd Super Target, a 2nd Pet Smart, a new Fleet Farm, a Lowe's, a 2nd Best Buy, a Dick's Sporting Goods, and several more smaller stores have all been built and opened in the southern part of town.
There are several smaller towns which are an easy commute from here - 30 minutes or less (and of course more).
As far as renting versus buying first, I personally would say rent first. That way you get a feel for the town, what area you would want to live in (although people may try to point you to the NW part of town, it's not all rosy like it used to be), or if you would rather live in a smaller town. There are properties here that accept pets. I'd say to find some of those, check out rent.com. They often will say what the pet policy is as far as dogs or cats or both and how many, if there are restrictions on breed or weight. I would highly recommend staying away from Hunter's Ridge Condominiums. They do accept pets but it is not a safe place to live.
Timberland Partners I believe at least one of their properties accepts pets. Also
The Gates of Rochester. I believe they both may offer leases that are less than a year as well if you wanted to go that route. That's a start but still check out rent.com to at least see what else allows pets.
Rochester doesn't get as cold or as much snow as the northern part of the state, but you can easily take a weekend trip up to Duluth or the North Shore and enjoy the winter up there. Odds of a white Christmas here are extremely high - although it's always possible not to have one too I suppose. The whole state is beautiful and it's a great place to live.
Good luck!! Just ask (or DM me) if you have any more questions.
