Based on your criteria, I think you’ll be best served by the Starwood Preferred Guest American Express. It’s what I use, and there are a couple more moving parts than with most rewards cards, so bear with me.
The SPG Amex gives you 1 “Starpoint” (i.e., a point in SPG’s reward program) for every dollar you spend. (And 2 points per dollar when you charge a stay at a Starwood hotel.)
You can exchange Starpoints for miles in most airlines’ frequent flyer programs. (Here’s a chart showing conversion rates; for almost everyone but Continental/United, the exchange rate is 1:1.)
BUT for every multiple of 20,000 miles you exchange at once, you get an extra 5,000 miles (i.e., a 20,000 transfer yields 25,000 miles, 40,000 yields 50,000 miles).
So, in short, each dollar you charge is worth 1.25 miles on most airlines’ rewards programs.
Now, what are those miles worth? Obviously, this depends on A) the cost of the flight you want, and B) how many miles it will cost you (which varies from airline to airline). I used an Excel sheet to simplify all this, and it’s yours for the asking. And if you do ask, skip the next couple paragraphs, as it’s so much clearer just to see the numbers.
Personally, I used two not-so-hypotheticals: a $500 RT flight to Hawaii (35,000 miles on American), and a $900 RT flight to Tokyo (50,000 miles). This yielded a cash value of $0.0179 per Starpoint and $0.0225 per Starpoint respectively. (Note: I also calculated the cost of a business-class fare to Tokyo, $5,500/100,000 miles, also on American, and got a whopping value of $0.078/Starpoint. My wife and I probably won’t ever use this – we’re fine with coach – but it’s worth keeping in mind.)
The card has a $65 annual fee, and to break even (versus a card that gives you $0.01 cash back per dollar charged) you’d need to charge about $5,200 (this is using my “coach flight to Japan” values). So if you’re going to be using your card for at least that amount, this is probably the one you want versus going with Telemark’s suggestion.
A few caveats: the math I did was using AA’s off-peak redemption rates (these use the fewest miles and therefore sell out the fastest). My wife and I will be flying back from our honeymoon in Japan using these tickets (booked about 3-4 months out, IIRC), but YMMV. Also, the miles don’t pay for taxes and fees; for our Tokyo to LAX flight, this was about $50 per ticket, IIRC.
FWIW, you can also redeem Starwood points for stays in Starwood hotels, but I haven’t yet found a situation where it would have made more sense to do this. (Basically you’d need an event such as, say, Comic-Con, to inflate room prices well past their normal range.)
If you’re interested in this card, feel free to PM me and I can send you a referral offer that’s good for up to 25,000 bonus Starwood points.