Does the campground have showers? If so, use them instead of the RV. Some RV showers dump into the black tank (and you'll use a lot of water). If not, do navy showers and use baby wipes to freshen up.
Use paper plates, etc., to limit dish washing. Buy bottled water to supplement for cooking and drinking.
As a solo person with minimal conservation efforts (other than no RV showering), I can go 9 days on a 40 gal fresh water tank and 20 gal grey and black tanks.
You might do a search for dump stations near the campground - there might be somewhere within a short drive where you can dump if necessary.
