the area drained better, but I don't see any easy way to put in drainage
tile or anything like that, without busting out the walkway. That might
be a project to consider next year.

Just an FYI, if you don't mind getting dirty... you can dig under a sidewalk
fairly easily with water pressure. Dig a pit down on either side of the
sidewalk, at the depth you want the pipe to go through.

Turn the garden hose to high pressure and just start forcing the water to
erode a spot of soil under the sidewalk, advancing the hose as it digs through
the soil. Eventually, you'll break through on the other side and can
thread your pipe (or wire or cable) through.

There are specialized boring tools that the guys that lay underground cable
and the like use for getting under roads and driveways... but the hose
method works well for small distances, and it's nice and cheap.