The more appealing and venerable parts of Old Town Tallinn are sadly not friendly to wheelchairs. Cobbles are the least of it – it's the stairs that link Toompea and the lower town, wind up many towers, and take visitors down into dank bastions and cellars that are the real obstacles. Some buses and other public conveyances are equipped to deal with disabled passengers; many are not.
It is law, however, that all new buildings in Estonia must be accessible to all, so shopping centres, newly developed museums and ferry ports won't be a problem. Some tour operators run accessible walking tours that may be an option: Sage Traveling is one.