First, I don't know what bonus you get on these categories, so I can't do the math for you.

Second, I don't know how much you value a UR point (because it depends on what you'll transfer it to and what you'll use it for then), so again I can't do the math for you.

I can illustrate the math with an example, however. Let's say you had a card that was 1% cashback, and 2% cashback in certain categories. If you spend $600/month in those categories, that's $7200 a year in an extra 1% cashback, so $72. Therefore it comes out even with a $72 annual fee.

Ie, you take the annual spend, mutliply it by the difference in rate of return (typically some number of cents per point) versus on another card (if you didn't use this one), and that gives you the break-even annual fee.

Obviously this is a lot simpler to do with cashback, because you know in advance what the value difference is. It's a lot harder to do with UR points you'll transfer to airline miles and/or hotel points, because it all depends on your redemption patterns how much those will actually be worth (and even then, it also depends on what cash prices would have turned out to be had you not used miles/points, which may itself be tricky to predict with accuracy).

Given all that dubious accuracy, I'd want to get a lot more value out than the annual fee, since if I only am getting "break-even" but my assumptions about the value of a UR points for me later turn out to be excessive, then it will later turn out that I didn't break even after all.

I myself don't carry any annual fee cards that don't give me a benefit that makes the annual fee worth it even if only do a little spend. (Benefits include primary-everywhere collision insurance on my Diners Club, free night certs annually on my Chase Prioirty Club Select Visa and Chase Marriott Rewards Premier Visa.)

I do spend a lot on travel, but find it more practical to, for example, earn 5 pts/$ extra by using the no-annual-fee or no-net-annual-fee hotel card specific to each program, rather than using one (Chase Sapphire Preferred) card for all hotels but earning fewer extra points. (I don't know what the hotel bonus is on Chase Sapphire Preferred, but I assume it's not 5x!) That works for me because 95% of my stays are in hotels that belong to hotel programs I participate in. And I live/work in SoCal (Los Angeles/Orange County), where I like it or not, all physical commuting has to be done by car! Finally, most of my paid travel is on one airline (AA), and I have an airline card that earns me 2x on that airline, and the bank (Citi) happens to credit back the same amount as the annual fee each year, so it doesn't "act" like an annual fee to me. (And it doesn't matter much which card I use on the fees I have to pay on award air travel, which may be on one of several airlines in my case.)