It will vary case to case, but there's a number of available revenue streams for U.S. states that have no income taxes (personal, corporate, or both):
Property taxes, as you suspect, are often higher but these are levied by municipalities and tend to make up for what would otherwise be funding flowing from the State-level government to the municipalities for things like schools, &c.
Sales taxes are also common, though some states (I live in Massachusetts, so New Hampshire is a perennial example here), have no sales tax.
Excise taxes are also common in one form or another. In the United States these are most commonly, gas taxes, tobacco taxes, alcohol taxes, and so on - these are assessed to the merchant, and so are invisible to the consumer which is why they're kept separate from sales taxes.
There's something called an 'excise tax' which is assessed to the consumer, and so isn't actually an excise tax, but instead a property tax, which is assessed on owned motor vehicles.
Down in the weeds there's stuff like license fees (hunting, fishing, driving, etc.), service charges (what you pay when visiting a state park to go camping, for example), estate taxes, property seized through civil forfeiture, abandoned property held in trust, and other financial esoteria.
Each state will address their budget in their own way, so which of these tools is used how much will vary.