If you plan on cancelling the card before the year is up to avoid the annual fee then are you looking for something specific? Like enough miles for a plane ticket somewhere? A Disney gift card? The best rewards card for regular use and the best bonus for opening a card may not be the same.
For example, I opened a Disney rewards card because I needed a Visa card and we were about to purchase a vacation to Disney. I got 0% interest for 6 months on the vacation, maybe $100 credit on my statement, and 2% cash back on the vacation I just purchased. I used the card regularly before our trip and had a few hundred dollars in a Disney gift card by the time we traveled. It worked out nicely for me but in the end it's not nearly the best rewards card out there. I still use it because I do like the flexibility on using any airline and not needing to use rewards points but can get a credit on my statement for the a portion of the fare or the full price of the fare depending on my rewards balance. Although I think my DH's Chase premier card gets better points to dollars.
We are going on a trip to the Dominican in March so my DH opened a United Chase card which gave us 30,000 points after spending $500 and we opened a Chase Premier card that gave him 40,000 points after spending $3,000 in the first 3 months. We used those cards regularly and ended up with 70,000 points which we cashed in for a free flight to the Dominican which was running between $600 and $700 over the last few months.
So...I guess the best bonus for opening a card could depend on what you would want.
I wouldn't open a bunch of cards and cancel them before the year too much because it probably isn't great for your credit score. I've done it before to get some airline miles but only once in like the last 10 years so it wasn't a big deal on my credit report.