If you spend more than $20,000 per year, get the Alliant Cashback Visa card. If you spend less than $20,000 per year, get the Citi DoubleCash.
If you have significant spend in dining and travel, you should consider the additional complexity of adding a second card. If you don't spend a lot on these categories, get the Uber Visa. If you spend $10K+ on these categories, get the Chase Sapphire Preferred. If you spend $30K+ on these categories, get Chase Sapphire Reserve.
If you also spend significantly on gas and groceries, get the Wells Fargo Propel card.
Which credit cards should you switch to?
Possibly none. If you are applying for a major loan (like a new home mortgage) in the near future, where the interest rate is dependent on your credit score, I don't recommend switching credit cards. Inquiries into your credit reduce your credit score, and the average age of your debt will go down when you get a new credit card. Any savings from switching credit cards is likely to get nullified by the hit to your credit. Wait for clearer days!
I made this mistake once. I found a way to optimize my credit cards that was going to give me literally thousands of dollars of points. However, I went to refinance my mortgage, and the small drop in credit score from opening new accounts increased the cost of the refinance by enough to offset the savings. Talk about jumping over dollars for dimes!
Assuming you are in a regular state of affairs, then it's worth looking at which credit cards are right for you.
The simplest reward you can get is cash back. That's right - simply get a percentage of your spending refunded every month. No complicated categories to manage, no points, no limits. If this sounds right up your alley, then you should consider
Alliant Cashback Visa. This card gives 3% on all purchases in the first year and 2.5% thereafter for a $99 annual fee. If you spend more than $20,000 per year on this card, it's the best cashback card. This card also makes sense if you have use it during travel to other countries, as there is no foreign currency fee.
Citi DoubleCash. This card gives 2% on all purchases with no annual fee. You get 1% at purchase and 1% at payment. There is no annual fee with this card. Note: foreign purchases are subject to a 3% fee, wiping out any cashback benefit.
Two other cards are worth considering if you have relationships at these particular financial institutions.
Bank of America Premium Rewards. This $95/year card gives 2.0% back on travel and dining and 1.5% back on everything else. However - if you have over $50,000 combined in accounts at the bank (including in their online brokerage, Merrill Lynch), you'll get a 50% bonus - equivalent to 3.0% back on travel and dining and 2.25% back on everything else. Have more than $100,000? The bonus will get you to 3.5% on travel and dining and a competition-beating 2.625% on everything else. Note: it's not worth keeping money in a dead checking account just to get this bonus, but if you have enough investments anyway and spend more than $20,000 per year, this will make sense for you. There is no foreign transaction fee.
Fidelity Rewards Signature Visa. This card has 2% rewards, no annual fee, and just a 1% foreign transaction fee. This is the card I use for cash back since I hold my emergency fund investments at Fidelity. The 2% rewards add a nice kicker to my account every month.
Consider a second card if you want to optimize further. Another reason to get another card is that you find you are able to use points at a higher rate than cash back. You want to get a card that matches your highest spend categories (often but not always travel and dining). This is easy to determine: input your normal spend here and it will recommend the best card combo: http://www.creditcardtuneup.com/
To keep it simple, you could just stop right there and get the recommended credit cards. For a deeper dive, here are a few credit cards I suggest as contenders for second wallet position.
Uber Visa Card. This is a great, no-nonsense, no-fee card for dining and travel. 4% back on dining, 3% back on travel, 2% back on online purchases. Although it's still 1% back on "everything else", depending on your spend mix, you might end up at 2% blended anyway. This is such an easy card that it might even be worth having as your single card.
Chase Sapphire Reserve, or its lower end cousin, Chase Sapphire Preferred. These offer 2x - 3x rewards on travel and dining, defined broadly, but have hefty annual fees. Generally speaking, if you travel more than a few times per year and will be spending more than $20,000 on the card, I think you should be willing to pay the annual fee. It typically gets credited back with airline fees and other perks like free breakfast at properties you stay at. By the way, it usually doesn't make sense to get two annual fee credit cards (likely best to pick between the Chase family and the Amex family since most of the benefits duplicate each other)
Why Chase instead of another program? The rewards points for Chase cards are extremely flexible and can be exchanged as either cash back, points exchanged for other travel programs, or travel purchase dollars used directly on Chase.com (with a bonus). Due to their flexibility, the points are generally considered to be worth more than $0.012/each. In fact, you can sell them to a broker like cashformymiles.com right now for that price.
Again, you need to be spending about $20,000 or more per year on these credit cards to justify the annual fee increase above the Uber Visa card.
If this is truly a second card, you might consider getting an American Express card which doesn't have as wide acceptance but have some other healthy features. The two best options are
Wells Fargo Propel Card - 3% back on groceries, dining, travel, and streaming - a nice broad list of secondary categories. This card has no annual fee and no foreign transaction fees.
American Express Platinum Card. Are you rich? This is for the heaviest and most luxury travelers. If you spend a ton on travel and like to travel in high style, there really is no match for this card. It gets you premium status in various programs like Marriott and Hilton, huge point rebates when you book with airlines or AmEx directly, and importantly access to Centurion lounges - exclusive lounges all over the country that are being built out quickly. While the annual fee is a steep $550, the Platinum usually comes with hefty sign up bonuses and tons of credits for services like Uber, Global Entry, and airline credits.
Also, AmEx points are the most valuable points of any program. The current going rate for just selling them to a broker is $0.0121/each. You can either take this path, or alternatively spend the time to use them yourself on AmEx's website.
Should you get a brand-dedicated travel credit card? For example, should you just get a United card or Marriott card? In most cases the answer is no; but if you are particularly dedicated to a provider (because for example, you live near their hub) then these cards might make sense. Overall I suggest keeping your options open with one of the other cards mentioned above.