Hi Annie,
I guess any Altera board can run Nios II. It really depends on your FPGA requirements and board needs, and target budget for an FPGA.
Stratix II is faster has more PLLS, mem, dsp than Cyclone, however the unit price is higher.
Most of Altera's boards are under $1000 and are good solid development kits.
If you don't have hard requirements on the FPGA or board, Future Electronics, who I am affiliated with, provides a good Cyclone II/NiosII board for $199. It should be available very soon.
Contact your local Future Distributor.
http://www.futureelectronics.com/contact/ (
http://www.futureelectronics.com/contact/)
-Baycool