In Downtown, I recommend Su's Express Alterations on Nicollet Mall.
Su's Express Alterations
(612) 659-1286
927 Nicollet Mall
Minneapolis, MN 55402
I had a bridesmaid gown that I needed to be altered within a few days of my sister's wedding, and I wasn't sure they would able to do it within such a short amount of time. However, the seamstress was able to make the alterations and did a FANTASTIC job. It was, for me, somewhat expensive - over $100, as I had extra work done to the dress. YMMV.
No suggestions for Eagan - sorry.