This summer, I had an internship and did well at it - I received a return offer, to come back as an intern again next summer. However, I'd like to see what else is out there.
Is it wise to note on my resume that I was offered the opportunity to return (showing that I did well), or will it come off as distasteful that I'm looking for other opportunities?
Is it wise to note on my resume that I was offered the opportunity to return
Unfortunately not. It's nice to be told that and it speaks to your work ethic but information like that does not belong in your resume, nor in your cover letter. Your resume should have more factual information than that, tied to your specific accomplishments. So you can say things like "consistently high customer satisfaction" or "reduced issue backlog by 80%". In other words, you should say why they were happy with you and offered you another internship, don't just say that they did.
You can and should mention this in an interview when you're discussing the internship and the fact that they were happy with your performance. I've actually done this myself when, after interning at a place for a few years over the summer, they offered me a full-time job after graduation. I didn't mention that fact on my resume but I did bring it up in nearly every interview when the internship came up. That combined with my manager there giving me an amazing reference and confirming that he wanted to hire me gave me an amazing edge over other candidates. This is also why you should ask your manager if he's okay with being a reference in the future.
Note that your fears of being seen as "ungrateful" are unfounded. Plenty of high-performers are in your position and choose to move on to different companies to get a wider experience. There's nothing wrong with that and you don't have an obligation to remain with an employer that treated you well.
