Hi Val, my daughter and I just returned from a week in Iceland…I have a couple of suggestions for easy activities that you can book as a day trip from Reykjavik. We did the Inside the Volcano tour which was expensive but very cool! Hotel pickup is provided, it's about a 30-40 minute drive, then a 45-60 minute hike to base camp. From base camp, you are taken down into the magma chamber of a long dormant volcano - I believe it's the only hollow magma chamber in the world. They lower you down on a window washer's platform and you get to walk around inside for about 45 minutes. Very cool experience and the hike takes you over the fissure between the tectonic plates as well.
http://www.extremeiceland.is/en/activity-tours-iceland/caving-iceland/inside-the-volcano
Another idea would be to go hiking or snowmobiling on a glacier. This would be about a two hour drive from Reykjavik. We did it from the town of Vik, on the southern coast, but many of our group came on a minibus from the capital. The snowmobiling was one of my daughter's favorite activities. The hiking was also cool - I loved that the water from the melting glacier was s pure that we could fill our water bottle up from the stream on the glacier! http://www.extremeiceland.is/en/activity-tours-iceland/snowmobile-iceland/adventure-snowmobile
This trip includes the hiking plus a bit of sightseeing - Reynisfjara (the black sand beach and basalt columns) was one of my favorite places of the entire week! And the waterfalls along that stretch of the coast are beautiful. http://www.adventures.is/Iceland/GlacierHiking/GlacierTripsFromReykjavik/GlaciersVolcanoesWaterfallsGlacierTrip/
We also went horseback riding, but did this on our own on the Northern Coast, so can't talk about the tour aspect of it. We did thoroughly enjoy our ride, however!
There are so many wonderful choices - whichever you decide, you can't go wrong! Just one word of caution - even though it's July when you are going, definitely pack a thermal base layer, waterproof hiking boots, and waterproof rain gear (both pants and jacket). The hike to the volcano was cold and rainy - they told us it was a "drop zone" for moisture:) And of course, snowmobiling on the glacier is cold - they gave us insulated coveralls, but I was still cold even with those and my base layer and waterproof clothing! It rained every day that we were there - we went at the end of May, I hope you get better weather! Have a great trip!