[Declining Graduate Offer From Your Undergraduate School?]

I'm having a hard time declining offers in general, but an especially hard time declining the offer from the school where I'm currently a senior (graduating in May). I know a couple of professors personally and respect them very much, I just think that I want to experience a different city and learn from a different perspective for my second degree. But this is causing me great anxiety, being afraid that I will seem unappreciative or disrespectful. Has anyone does this before or have any advice for handling this and maintaining good relations?