Angel Stone isn't bad if you want a fairly simplified version of Diablo with a bit of online/community stuff. It's not quite at the simplicity level of a cow clicker, but does have a bit of grind in it like all Diablo-style games. Fortunately they've simplified that a lot, with blitz tokens (buy lots of permanent ones early on) and even auto-play for when you're just burning off resources or leveling on earlier stages. So far I haven't found it to be p2w, and have a lvl40 build within 5 days of playing that will more-or-less see me through the rest of the game. It does have a stamina system, but it's pretty lax on what restraints it gives you. You can play on PC under Facebook if that's your thing. It does make it way easier simply due to responsiveness and hotkeys/mouse control.
Superior Tactics RTS is also pretty fun in its earlier stages. It's a 2d side-on real time space game, where you construct a fleet with various weapon/shield/utility layouts and take on a bunch of different challenges in missions. It ends up as a shit-heap leader board grind in pvp if that's what you want to do, but it's not too bad up until that point. Has some FPS issues, but mostly in pvp or BIG skirmishes. It has the underlying basics of being a great game, but only ended up as average/good in its current form. Not p2w at all, though there are options for it, it just speeds things up a tiny bit and would be a waste of money. Ad supported, but just close them at start of mission and you've got a free game that's actually pretty good until the pvp part.
There's a free version of HoMM2 called FreeHeroes2 out there that works pretty well, and a version of HoMM3 called VCMI as well. HoMM2 works reasonable well, but combat positioning can be tricky. "Kind of" needs a copy of the full game, but it can get by on free demo-disk resources if you don't mind losing a few options (the game happily downloads these for free for you). There's always GOG or abandonware for the full version and expansions (I do own a legitimate copy, but the disks are broken. And it's quicker to d/l off the net these days anyway).
FreeCiv is good. Just like Civilization 1 or 2, but free. Pretty simple to use interface, but takes a little bit of time to work out the terrain improvement icons. But if you want Civ, here you have it. A fair few scenarios included as well. Starting with an explorer is a work of genius to speed up the early boring bits.
The two best games for mobile IMO are the NES versions of Pirates! and M.U.L.E. They're great. Download an emulator (Nostalgia.NES is free) and play until your heart's content. NES controls work pretty well on touch screens, both games have very simple menu systems that are quick to use, and both are great games in their own right. Not too reflex orientated, even while being RT. Can be a bit repetitive, but with emulator save/load, they're great for lunch breaks and still very replayable to this day.
On the emulation front for something that you might not consider, some sports games work surprisingly well on touch screen. Here's a few that I've tried and the system they're from, or the best versions of them IMO: California Games (SMS and Genesis), Madden '97 (SNES), PGA Tour 95/96/97 (SNES), Brutal Sports Football (Genesis), Madden 2001 (PSX, using RetroArch emulator, 3D graphics!), Tiger Woods Golf 2001 (Gameboy Advance/RetroArch), Tekken 3 (PSX/Retroarch, it's a slightly slower fighting game).