By the bullet train (I'm assuming you're not going for the cheaper but longer bus rides since you're only there for 7 nights) it'll cost over $100 each way to Osaka and back, and I think it's close to that as well to get to places around Nagano. Not sure about your exchange rate, but for me the 7 day pass was $320 which makes it definitely worth it just for those trips. Just remember you'll have to bring some extra cash for travelling off the JR lines and you should be all good