As an undergraduate at the U of MN (Go Gophers!) who has done some research at the IMA in numerical PDEs, I have a very high opinion of the department and its staff. The IMA is a great facility (with newly renovated offices and first floor of the building) with friendly and intelligent faculty, as well as a number of new and well-kept computers. The proximity to the supercomputing institute would also certainly be a boon, in the event you have extremely high complexity computations to perform; and there are many yearly conferences that take place that bring in some of the birghtest minds from across the country. Furthermore, there are some very bright (and fairly young) minds studying dynamical systems and differential equations here, so there should be a good number of people to bounce ideas off of.
The only downside to the U, in my opinion, is the state of the mathematics building itself (Vincent Hall). It is rather old and hasn't seen any significant renovations in quite some time, outside of the occasional new paint job. The math library it houses is fairly substantive, though, and the building isn't exactly in disrepair. In all, the U is a great program; although I have little to compare it to, I sincerely doubt you would regret attending if you have a great interest in numerical PDEs.