I'll agree with you that Robert Jordan's longwindedness left a bad taste in my mouth and initially made me shy away from starting this series, but having read all 4 extant Song of Ice and Fire books, I will be the first to say that, compared to Jordan, George R. R. Martin doesn't let his story ramble. While Jordan started out strong and then let his wheels spin for about 6 or 7 books, Martin is actually trying to accomplish something with his tale.

Catelyn loves her sister Lyssa and didn't know she had lost her marbles. Catelyn has been stuck up in the North for something like 16 years. Lyssa wrote her to tell her she thought her husband Jon was murdered, and Catelyn believed it because shortly after, her son was nearly killed by Lannisters. We see our family through different eyes.

So Catelyn thought her sister would believe her, and being the dowager of a whole kingdom, Lyssa would have the authority to try Tyrion. Catelyn did not capture the imp in the North - she caught him on the road as he was heading South and she North.

As for the political implications, that's tricky. King's Landing is out - the Queen is a Lannister, and Catelyn knows how scummy that place is from her last visit. That leaves 3 other choices: Winterfell, Riverrun, and the Vale/Eyrie.

Why not take him back to Winterfell? Tyrion explains that one indirectly: He thought she was taking him North, and warned that his father would surely send people to find them on the road and overtake them. When she took off the bag, he was surprised that she wasn't heading North and complimented her cunning.

She's a Tully, and their words are Family, Duty, Honor -- so why didn't she take Tyrion to Riverrun (the Tully capital city)? Probably the same reason: Riverrun is in the direction of the Lannister lands, so they may be overtaken. Now she may have been able to get to one of those knight's or bannermen's homes, but that might be bad for other reasons -- Tully and Lannister lands border one another.

So she weighed Riverrun and the Vale/Eyrie, and chose her sister over her hometown, probably to avoid being caught by Lannisters.

Go to HBO's Viewer's Guide for Game of Thrones to see a great map. I linked to the Inn where the capture takes place. You can follow the roads from there: To travel to Riverrrun, she would be heading toward Casterly Rock (Lannister capital). The Vale is clearly the closest place where she has allies.

Brilliant reply, thanks! More than I could have hoped for.