I need to convert databases both directions and I also need to grab subsets of data on occasion. Is there an easy way to do this?
Set up a DSN for your MySQL database.
To import, choose GET EXTERNAL DATA | IMPORT from the FILE menu.
Pick ODBC and then the DSN as your data source, and choose the tables you want to import.
To export, choose EXPORT from the FILE menu, point to the DSN for your empty MySQL database and choose the tables you want to export from Access to MySQL.
My answer assumes, based on your asking about exporting and importing, that these are one-way operations.
There are Many programs that can do it. dbload is an example. I haven't found any database converter freeware yet.