A 2003 Suburban's fuel tank capacity was typically around 26 gallons. However, even knowing this, the mileage per gallon is the crucial missing piece. You might see anywhere from 12 mpg (city driving with a larger engine) to perhaps 18 mpg (highway driving with a smaller engine and careful driving).
To estimate the range, you would multiply the fuel tank capacity (approx. 26 gallons) by your Suburban's miles per gallon (mpg). For example:
* Low estimate (12 mpg): 26 gallons * 12 mpg = 312 miles
* High estimate (18 mpg): 26 gallons * 18 mpg = 468 miles
In short: You could potentially get anywhere between 300 and 500 miles on a full tank, but the actual range will depend on the factors listed above. The best way to know is to check your owner's manual (for the specific engine in your Suburban) and then monitor your own fuel consumption.