We have a two-bedroom house near Tartu booked for 20 June through 08 July. We'll be leaving Helsinki on Thursday 29 June, staying in Tallinn on that night. We'll return to Helsinki on 08 July. I'm happy to give rides.
One item to keep in mind when choosing your options is that Tallinn is a very small station for the rental car companies. European rules are that if you are more than two hours late for your stated pickup time, your reservation is null and void. We found out the hard way last year. Our options were Rīga or Helsinki, nothing in Tallinn for the entire week.