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Filmore county hasn’t any natural lakes but the county does have a few abandoned iron ore pits that have fish. Do an internet search specific to the county to find out who owns them and ask permission.
North of Rochester about 12 miles you’ll find Lake Zumbro and within Rochester’s city limits there are lots of retention ponds and the Cascade Lakes Complex. Silver Creek, KR5, Willow Creek, Whistle Binkies South pond and others are all retention waters found in the city and all of the above are panfish hot spots. Size can be a challenge, but Silver Creek, Cascade and Lake Zumbro all have some decent fish. There is also Foster-Ahrend Lake where some dandy trout can be caught….you do need a stamp to possess [keep] the trout.
If you want some real diversity, take the trip east to the Mississippi River backwaters found in lower pool 4 and in pool 5. This spans from Wabasha to below Kellogg, Minnesota and across the river to the Wisconsin shore. The dike road to Wisconsin from Wabasha is a great place to start. Just below Wabasha is Wilcox Landing. A bit further south will bring you to the Finger Lakes area along and below the actual dike which separates pool 4 from 5. Further south yet will get you into West Newton Landing area and the Half Moon Landing areas…very popular.
Winona offers a lot of ice fishing on the many lakes they have, especially the two at the large park along the highway on the south/east side of the city.
Do a google search of maps for these areas. There is a lot of water not far from you, but Filmore County is one of the water-poorest counties in the state outside of trout streams.