Hey Brosius,
The Miyata 610 was second in Miyata's touring line behind the 1000. They are generally very well regarded pieces of machinery. Miyata is known for it's high manufacturing and quality standards and was one of the major manufacturers during the Japanese manufactured bike's high times. Depending on condition, size of the frame, model year, and components, I would guess that the value could be anywhere from $250-$400 with the right buyer. Miyata has quite the cult following, especially for their touring bikes. The "rubber cushion" or brake hoods that you refer to can be replaced but, depending on the model of brakes, can be hard to find and very expensive. There are often reproductions available at a lesser cost than new old stock originals. I find the best place to find them is on ebay. If you could post pictures it would give a better basis for evaluation, but given even moderate condition, I would consider the 610 a fairly desirable bike for touring applications