You asked about music .. looks like there is a free downtown concert on Saturday.
Bud Light Downtown Live Concert :: Downtown Raleigh Events
I tend to use triangle.com to find events.
About
Hillsborough Hog Day-- quite a fun time

(I love community events) -- go early so you don't miss out on the pig. And they usually have an excellent Elvis tribute performer, but it looks like he's not going to be there this year.
North Hills Mall area has outdoor music on Thursdays (Shag on 6/19).
One of my favorite things to do is Movies on the Lawn at the
North Carolina Museum of Art. They have a whole calendar of events and a great walking trail (paved). The movie on 6/20 is about space travel to the moon (not my cup of tea, but ...)
As you'll be alone you might consider looking into the Meetup groups to see if they are doing anything while you are here as its purpose is for singles to meet. I've never participated, but I've heard good things about it.
If you'd like you can e-mail me offline and we can chat .. I'm a very active single woman (early 40s) who's lived here since 1992 and I've probably attended every museum or venue in the area. Also I'm very good at finding info. If you give me an idea of what you want to know -- music venues, arts & crafts, theatre, parks, kayaking, canoeing, hiking, mountain biking, swimming, dancing, dining, ice cream, museums, bookstores, etc. I can help. My weak spot is nightlife -- I stopped the bar scene about 5 years ago, but I still know where to find those places.

But if you're here by yourself you probably won't go barhopping by yourself .. or maybe you would .. hee hee.
(You mentioned yoga .. there seems to be two outdoor yoga events and one business event ...
City of Raleigh Human Relations Commission Yoga in the Park - 6/14 10-12 a.m. Nash Square, downtown Raleigh. Rock out to Yoga - YogAsana South .. summer solstice party 6/21 9-5. Yoga in the Park - 6/15 7:30 a.m. to 8:30 a.m. Lake Shelley)
If you are staying in Raleigh and you don't have time to get over to Durham, you could consider the
JC Raulston Arboretum - Home Page instead of Duke Gardens. Now, I love Duke Gardens (and a visit to Duke Chapel), but if time is a concern the Arboretum is a good option.
Have fun ..