There are plenty of museums to visit in Raleigh itself - the link above will provide you with an idea of where to visit if anything interests you. The most popular spots are the North Carolina Museum of Natural Sciences and North Carolina Museum of History however the Marbles Kids Museum is also popular for a younger audience.
For the budding golfers out there Apex and the local area has plenty of courses you can get in contact with about tee times and prices. A popular course is Knights Play which has the extended house and Par 3 elements too. The link above has a list of golf courses in the local area.
Jordan Lake is one of North Carolina's largest state parks located 15 minutes west on highway 64. There are plenty of natural spots here to park up, chill out, relax on the beaches or even hire a boat and navigate the waters themselves.
Believe it or not you are able to get from Apex to Durham without using a vehicle - the safest and easiest way to do so if by accessing the American Tobacco Trail. https://en.wikipedia.org/wiki/American_Tobacco_Trail This is another scenic outdoor activity for those who wish to get their steps in, running along an abandoned railroad bed originally built for the American Tobacco Company in the 1970s. The closest access point from Apex is at Wimberly Road just off highway 55. https://www.google.com/maps/place/Wimberly+Road,+North+Carolina+27523/@35.7451562,-78.9204788,6725m/data=!3m1!1e3!4m6!3m5!1s0x89aceca5588b88c5:0x415d87ca6c225e69!8m2!3d35.7589129!4d-78.9190695!16s%2Fg%2F1tjdmm6j?entry=ttu&g_ep=EgoyMDI0MDgyOC4wIKXMDSoASAFQAw%3D%3D
If you're a fan of the coast and of film/tv then a day trip to Wilmington will tick these boxes. Nicknamed 'Wilmywood' or 'Hollywood East ', the city is located just over 2 hours south of us on I-40 E. There are plenty of historical locations to visit and with the cooler autumnal temperatures taking a stroll around the city will be comfortable for most.
Another professional sport that will have just kicked off by October - the Hornets will be at home for several games around the wedding week so if any people fancy a trip to watch them you can - similar journey time as the Panthers (2.5 hours each way).