The PSR-S770 and S970 are older, discontinued models, which is why you won't find them on Amazon, Guitar Center, or other vendor websites unless they are used or new old-stock. They were replaced by the PSR-S775 and S975, and then now have been replaced by the PSR-SX700 and PSR-SX900, though the Yamaha website still lists the S775 and S975 as current. Depending on the discounts you can find, the S775 and SX700 are going to be in the $1300 to $1500 range, and the S975 and SX900 will be in the $2000 to $2200 range. The PSR-S670, however, is around $800 to $850. So, that is something to consider, as well.
Also potentially important is, as the model numbers suggest, the S670 came out around the same time as the S770 and S970 and is a 5 year old model. For some reason, Yamaha never came out with an "S675" version, and they have yet to come out with an "SX600" or other replacement/upgrade, but again, as this model is 5 years old, they may be planning something -- but that is just a guess.