(I see you've already accepted an (excellent!) answer, but I wanted to add a suggestion for declining should you need it in the future.)
The main thing to keep in mind is that your aunt thinks she is doing a nice thing for you, even if it doesn't feel that way to you. And based on your comments, it's quite possible she simply enjoys your company and wants to spend time with you - assume good will first!
If you are set on declining: To be tactful, it will help to acknowledge her good will and frame your conversation in a way that sounds like "it's not you, it's me". If there are other reasons you don't want to go, you could use those, but you don't necessarily need to explain. Finally, express your wishes for not being invited this way in the future. For example,
Dear Aunt, thank you for the invitation but I've changed my mind about going to the parade. How about I let you know when I find an interesting event to go to together?
- Declining this invitation
- Not accusing her - keeping the conversation positive
- Taking control of arranging future outings
Now, "tactful" and "direct" are often at odds, so it can help to be a little indirect to allow the other person to save face. You may need to repeat a few times, but after a few rounds of declining she should get the message.
If this doesn't suit your style or if she persists, you can try addressing the situation directly. However, since she has not actually told you why she invites you to things, talk about that first. Don't make assumptions, just ask why. Perhaps she will confirm your suspicion - but perhaps it is something else, like she misses you, or is lonely, or just happens to find a lot of events that she thinks you'd like. Once you know her motives, you can address the root issue and work from there.
Personal experience: I have gotten such invitations because I am very introverted and what you might call a "homebody". I am generally content with my social life but some people assume otherwise.
For example, my sister once asked me to dinner after we hadn't spent time together in a while. After I accepted she also invited a few of her friends, and at the dinner, in front of them, said she had invited me because "I figured you didn't have anything else to do!". I was rather hurt hearing that, and made excuses the next few times she invited me to things with her friends, in the manner that I described above.
(We eventually talked about why I didn't want to hang out with her friends, and among other things I made the mistake of directly saying that it felt like her invitations were out of pity. She felt attacked by that and the conversation did not go well - which is why I advise leading with a question instead.)
On the other hand, when the person has not been explicit about pitying you, and it's something you would otherwise like to attend, I encourage you to make the most of it! Another experience: I was recently on a business trip with coworkers I didn't know well, although they all knew each other. During a break, they were making plans to go out together for dinner in front of me, and kind of awkwardly tacked on "Oh... Em, do you want to go too?". I'm sure I wouldn't have been invited had I not been sitting near them, but I accepted anyways - it ended up being fun, and I have a couple of new office friends now :)