Three of us will be traveling to Ephesus and Cappadocia in June. We will be flying between each area.and staying for 3 days. Should we rent a car? Also we would apppriciate any recommendations for tour guides in Istanbul and the other two areas. Thanks.

You do not need a car for either location. A taxi from town will take you to the Ephesus site, it's not far. A guide with tramsportation will get you to see the main sites of the Cappadocia area. We had a car that allowed us to wander farther afield and drive between the two areas to visit Aphrodisias and Hieropolis.

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Do you mean staying three days in each area or a total of three days split between them?

I don't have a specific recommendation for a tour guide at Ephesus, but would encourage you to make sure that you see the Terrace Houses.

IMO, there's no need for tour guides in Istanbul or Cappadocia, unless it's your preference to work with one.

I agree with Michael -- no need for a car if you are flying between these destinations.

Thanks for your quick responses. We will be in Istanbul for 5 days and the other two areas for 3 days each. We are really looking forward to this bucket list trip.

Share what your plans are. We did not use a car in Cappadocia but did have our hotel arrange a driver for one day: we visited an underground city while he waited, then he dropped us at one end of the Ilhara gorge and picked us up at the end. Then we stopped at Selime monastery and visited a mosque as well, plus a couple scenic stops. The other days we hiked around and a car was not necessary. Having a driver ensured we could do the one-way hike through the gorge--a highlight.

Oh, I thought you meant 3 days for Cappadocia AND Ephesus! If you have SIX days for those two locations, then you might want to rent a car to see more of Cappadocia. Personally, I'd shift 1 night from Ephesus to Cappadocia, but of course, that depends on what you want to see / experience. If you haven't already seen my ancient trip report, you might find some information of value in there:
Some Observations on a Fantastic Journey through Western Turkey

Oh, and drivers aren't necessarily the only way to hike area gorges one-way -- for the Ihlari Gorge (recommended!), one of the staff of my hotel drove separately to lead me the way to a parking lot at one end and then took me to a starting point at the far end. Of course, I doubt every hotel would do that....