I currently practice Tai Chi (Yang style--short and long form) at an intermediate level. I enjoy it, but have recently wanted to explore a martial art form that still stresses economy/fluidness of movement, is well suited for an older adult (60's and in good health), but has a greater emphasis on not-too-demanding strikes, blocks, locks and learning to fall properly. I'm uncertain if Aikido fits this description--as I would like to pick up some practical self-defense techniques in the near(er) term--and Aikido classes are not offered near where I live. Hapkido, however, is. Would this martial arts form address many of my interests and needs? Would my practice of Tai Chi likely help or hinder a transition to learning this form? Finally, (and primarily out of curiosity), does Hapkido include forms for using a staff or other traditional weapons?
So you're in your 60's, in good shape, and you've been practicing Yang style Taiji. You're now looking to branch out and train in a style that has an emphasis on practical self-defense, which should have a mix of striking and grappling.
First let's talk about the age thing. Being in your 60's doesn't necessarily mean you can't do certain martial arts or are limited to just a small amount of low-impact styles. But it does mean you have to be aware of your own limitations when you're doing them. That's all.
You just have to make sure your instructors and partners know what you're comfortable doing. Either directly or through peer pressure, you're going to be tempted to do stuff that you know might be risky. Your best defense against this is to know your limitations and say "no" when you need to. Speak up. They can't read your mind.
That advice actually applies to people of all ages.
Second, let's talk about Hapkido and Aikido, since you brought them up. No doubt you've seen both styles, either in person or on the web. You're attracted to the joint locking and the effortless looking throws. You notice the fluidity of the motion and how everything seems to come from the "center". And you've seen a good number of older people in Aikido classes. This might evoke comparisons with the Taiji you've learned.
While Aikido has some strikes, Hapkido has a lot more and is much more developed. Hapkido generally borrows its striking from Taekwondo. While Aikido's strikes are merely used to distract ones opponent, Hapkido's strikes are done with the intent to harm.
As for its grappling, Aikido also has less number of grappling techniques compared with Hapkido. Though, some would say that Aikido's grappling is more refined in comparison. This judgment is biased, however, because Hapkido's objectives and training methods are much different from Aikido's.
Aikido's training method revolves around the notion of not resisting. And Aikido's highest moral code is to leave their opponents unharmed. Both of these contrast with Hapkido, which trains with a greater amount of resistance and with no reservations about harming their opponents. As a result, Hapkido will look a bit more "clunky" compared with Aikido. That arises directly from their values.
Aikido students are taught not to resist anything done to them. As a result, the throws and joint locks can look a lot more fluid and soft compared with Hapkido. Students of Aikido are often guilty of being too compliant, even throwing themselves into their partner's throws.
I talk more about Aikido and its weaknesses and strengths here:
The "do no harm" principle of Aikido means that hard contact beyond distracting strikes are not practiced in class. And without the need to develop striking technique, there just aren't a lot of strikes taught in Aikido.
So if your goal is to learn more practical self-defense, I would steer you towards Hapkido more than Aikido. Hapkido trains with more resistance than Aikido does. And Hapkido's striking and grappling is more complete. Based on that, I believe Hapkido is more practical for self-defense.
As for how Taiji training might help or hinder learning Hapkido or Aikido, I think you'll find that the styles are so different from Taiji that it won't matter at all. It will not be confusing.
I will say that Aikido is more compatible with Taiji, and that's because Aikido is a style that bases itself on internal mechanics, just like Taiji does. But Hapkido does not. As a result, you might find that transitioning to Aikido will allow you to continue to develop and apply your internal mechanics that you're learning in Taiji.
But a word of warning regarding internal mechanics: It takes 10 years under a very good, qualified Taiji instructor to learn internal mechanics properly and begin to use them in real life self-defense. It might take 20 years before you reach the point where you can actually use it "for real". So, are internal mechanics important to you? Or is it more important to learn practical self-defense that still uses good mechanics and leverage, but just not "internal" mechanics? That's a question you have to answer for yourself.
Your last question has to do with whether or not they teach staff and other weapons. Yes, Aikido teaches primarily the Jo staff (a 4 foot long staff), and also teaches sword and knife. Whereas Hapkido also teaches those along with stick, cane, long staff, and other weapons.
Finally, I'd like to recommend that you also check into Gracie Jiujitsu. It is very grappling oriented and specializes in ground fighting (wrestling). It also has a good number of take-downs, throws, and standing grappling. And while at first you'll learn defenses against strikes, later on you'll develop your striking a lot more. Their striking methods come from kickboxing and western boxing. Their primary focus is on self-defense, while competition is also done later on. They train with much more resistance, so it's going to be more practical and realistic compared with Hapkido. Will it be too physically demanding for you? That's a question you'll have to answer yourself.
Ultimately, which martial art you decide to take is going to be a completely subjective choice. My recommendation for anyone in this position is to go ahead and dive right in. Go to a school near you, and ask to try some classes. Usually schools let you try a class, or a week or a month of classes, without paying much or committing to anything. So go try some classes in one school, then another, and so on. This is going to answer all of your questions much more than reading what others have to say. In the end, you'll select the school that felt better to you.
Hope that helps.