You could walk to Oz Cafe at 8305 Broadway. Love their bubble tea. Head west on Roosevelt 4 blocks or so then go left on Whitney all the way down to Broadway. Left on Broadway about a block and you're there. Should take 15 mins or so.
Not that one either, however, the Elmhurst Ave station on the GVR lines (about a 10 minute walk from the 7-line Elmhurst/90th station). On Broadway there are several bakeries and I'm sure some of them have bubble tea.