Minnesota had non-partisan legislative elections until the early 1970s.
New Hampshire has an interesting electoral system in its state house. I forget the name of the system... but you have multi-member districts.
3rd party candidates have had some success in New England and Minnesota and 3rd party movements have always been relatively popular here.
NJ has multi-member districts, as well; each legislative district elects one Senator and two Representatives.
Washington (And Arizona IIRC) have the same system.
As do North and South Dakota. Although SD has a few districts split in half which each half electing one Representative probably for VRA reasons (all are districts that combine a Reservation with uber-Republican white areas.)
West Virginia has a rather odd system of apportioning the legislative districts, or at least the House. Maryland's is kind of unique too.
