As best I see it, you don't file a separate Grand Rapids return, rather, your employer withholds your tax and pays it directly to the city. This, however, is reported on the Common City Form CF-1040 which IS on your state return. TurboTax generates the CF-1040; however, it does not support e-filing it. I do not know why.
What you might try is this (no guarantees). After you pay for the Online product, you will be able to see all your forms, including the CF-1040 (and others?). Look at the Grand Rapids Income Tax webpage and go through them to see if you can find a phone number. Call the City and ask if you can mail the CF-1040 to them while you e-file to the state.
If they are OK with this, then before you file, go into The Print Center in TurboTax Online, create the PDF for the return (you should make a copy of the return in any case), make a copy of the city's form or forms, and mail them to the city.
Then in TurboTax, go to the interview for Michigan, on the left click on Tax Tools, then on Tools underneath it, then in the center, click on Delete a Form. In the list of forms find the CF-1040 (and any other city forms) and delete it. Then perhaps you can e-file your state return.
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