I've had Schwab as my main bank and investment provider for about 5 years, no complaints so far. I've transferred to/from Ally, a local credit union, and a few credit card/utility companies with no issues. I also rolled over a 401k from a previous employer into an IRA no problem.
Not only are there no international ATM fees, but no access fees either. Those $5 fee ATMs at festivals or whatever are fair game with a Schwab account because they refund all fees. I've called customer service a couple times about things I don't remember, but do know I had a good experience. Their ERs are really close to Vanguard, I think last time I checked they were lower than standard share fees but higher than admiral share fees (depending on the fund, and it's by .02% or something like that).
Only downside is you can't deposit cash, and the physical branches don't deal with banking, only investments. Banking is online/phone only, or at least it was a year or two ago when I went in with my girlfriend to help setup her IRA there.
The big strength of Schwab is for those starting out, as their minimums for investments are way lower than Vanguard (again, they were a year or two ago things may have changed). Vanguard has something like a $1000 or $3000 minimum for most investments, and admiral shares are $10,000. Schwab is around $100 minimum and lower than Vanguard's standard share ER. Having your paycheck go straight to your Schwab checking also makes it easier to transfer some to an IRA or investment account. There's no waiting for 2-3 days for a transfer to go from Ally to Vanguard or wherever. Not a big deal, but a small convenience.
The checking account is most likely a loss leader to get you into their investments (they make you open an investment account when you open a checking account, even if you never put money in it). It's a great deal, and I'm surprised more people don't use it.