I've been dancing around this myself. I already own a Leatherman Wave with Allen bits, so that was my first choice, but it is heavy. It does take the place of all my other favorite trail tools, plus a file, pliers and wire cutter.
Some of the big bike multi-tools strike me like a Swiss Army knife with too many layers. Simpler is better I think, so something like the Crank Brothers M10 has all the goodies you really need for field repairs. You can get into the same what-if game as hiking gear: at some point you're going to have to walk it back to the car. Likewise, a chain tool seems more like a bench tool to me and not much use unless you have a spare chain or carry a section of chain. I'm more on the touring side than single track, so I'm not that hard on chains.
Another way to go is a Swiss Army knife with a Phillips screwdriver plus whatever combination of tools you like, and just add a collection of Allen wrenches to match the fittings on your bike and wrap 'em up with a rubber band. As with the Leatherman, you get all the hiking tools and you can tweak any fitting on the bike short of replacing stuff you wouldn't be doing in the field anyway. I can handle just about anything on my bike with 3/4/5/6mm Allen bits and a Phillips. In fact this is just what I handed my daughter for her repair kit.
You can get a short stack of Allen keys pretty cheap. The thing with a classic Allen key is that you get a lot of leverage for the weight and cost. Get the ball head version and you could adjust something halfway up your nose :)
The multi-tool I lust for is the Fix-It Sticks, with two hex bit holders that combine to make a tee wrench. I love the clever design and they take standard bits, so you can tweak them to suit your needs. They are, of course, too expensive (30-$35) for just the novelty. There have been many hex bit holder gizmos made over the years, with a driver handle of some sort holding hex bits inside.

For flats, yes to good simple plastic tire levers. I have the one with three in a sleeve. Add small patch kit, CO2 inflator (I got one cheap) or a pump and a spare tube. I like the spare tube thing: think pouring rain, dark, side of the road, glue dried up, etc, etc.
The best urban repair kit I've heard of is a good lock and enough bus or taxi fare to get home :) You're going to have the lock anyway….
If I'm home, I like "real" tools like full sized screwdrivers and Allen wrenches with ball heads. Then there are all the specialty wrenches for getting in tight spots, weird spanner nuts and the like. I gather those only when needed. I like tools and they stick to me better than hiking gear. After decades of cars, motorcycles, boats, home construction and remodeling and living in the same house for 30 years, it's the tools that challenge any thoughts on "simple living." Keep it simple!