If you want to stay away from Citi, have a cashback card, and need it to be a Visa or Mastercard, I'd probably recommend the Chase Freedom or the Bank of America Cash Rewards.
With the Chase Freedom you'll get 5% on up to $1,500.00 spending on rotating quarterly categories. They change from year to year but for example for 2015 the bonus categories were:January - March:
Grocery stores (excluding Walmart and Target), Movie Theaters, StarbucksApril - June:
Restaurants, Bed, Bath & Beyond, H&M, Overstock.comJuly - Sept:
Gas Stations, Kohl'sOctober - December:
For everything else (or for purchase over $1,500 per quarter in the bonus categories) you earn unlimited 1% cash back.
With the Bank of America Cash Rewards there are no quarters and you earn 3% cashback at gas stations (limit $1,500 per quarter), 2% cash back at grocery stores (limit $1,500 per quarter), 1% on everything else unlimited.
Both cards have no annual fee and are Visa cards. If 'premium' is a concern, the BofA is a Visa Signature which does come with some added benefits and protections compared to a regular Visa card, although I believe most/many are geared toward travel. I think one more widely applicable benefit is extended warranty protection. I think there's also a way to upgrade the Freedom to a Visa Signature, but I might be wrong.
If the new card doesn't HAVE to be a Visa/Mastercard, I absolutely recommend the Discover It.
If you're okay with a Citi card you might consider the Citi Double Cash, which is a great way to earn unlimited 2% cash back on all purchases without worrying about categories. You get 1% when you purchase something and another 1% on all your payments. The Double Cash is a World Mastercard which, like the Visa Signature, offers additional benefits and protections compared to a regular Mastercard.
I have all these cards and love them.