MicroProse's F-19 is the flightsim I played and enjoyed the most, and it wasn't realistic.
If you download DCS World directly from the site instead of getting it through steam, you can get a 2 week trial of each module every 6 months.
Flaming Cliffs 3 is the name of the less realistic module. It comes with several planes or you can buy them individually. As I said before, you can try them all for free for 2 weeks each and it resets every 6 months.
Actually they have an iOS version, which isn't bad, except the lack of joystick support.
If you used to love GraphSim's F-18, definitely do check out Tiny Combat Arena. It has the same vibe!
MicroProse F-19 hit that awesome spot of some realism (laughable today, but it wasn't meant to be an arcade game back then), with a really easy flight model and cool missions and scenarios you could really complete. And besides knowing the keyboard mappings, you really didn't need a manual. It was thrilling to play mission after mission, getting all those medals, and having your character be promoted in rank. I spent a lot of time with that game -- probably flew as many missions as an actual combat pilot!
The only other flightsim I found almost as engrossing was Gunship 2000, with its "dynamic" campaign system, but it was way more difficult.
I find Tiny Combat Arena captures some of this thrilling but simple gameplay, but it currently lacks content (more campaigns, more maps, more things to do).