Online searching is the best way to start. Sites like this are good, the only thing is that sometimes current information is delayed in posting and not all available properties are listed. A good way to get ALL the available listings as they are listed is though a larger Real Estate company website like my broker's site CBBurnet.com. The search capabilites have a broader range, too. You can also create your own account and have the same MLS on my personal website below. A good place to start in the south half of the Twin Cities may be Eden Prairie, Eagan, Minnetonka, Edina, West Bloomington, Burnsville and Mendota Heights.
Realtors have direct access to the MLS allowing more search criteria and more property information that is available to the public. I did a quick search and there are absolutely beautiful homes in fantastic areas that fall within most of your search criteria. If you would like to send me your email, I can send you this saved search or even set you up with an automated search that will send you new listings with chosen criteria as they are posted on MLS for an indefinite length of time.
Good luck on your search and feel free to contact me diretly at any time!
Coldwell Banker Burnet
I tried sending an answer earlier but it doesn't appear to have gone through. I appoligize if 2 show up in the answers!)