I would DEFINITELY DEFINITELY take a baby carrier with me. Sometimes kids get tired of being in the stroller and want the personal contact with mom and dad, and it is SO hard to push a stroller with one hands while carrying a child with the other!!
To cut down on the hassle-factor and make the carrier earn it's keep, I would get a soft structured carrier. This is the kind with straps that go around your hips and your shoulders and carry your baby upright, but does not have a rigid metal frame. They are easy to fold and stick in the stroller basket when you're not using them.
My absolute favorite is the Beco Butterfly carrier. I used it almost daily with my daughter (now 2 1/2) until I got pregnant and too big to wear her. It is well padded and balances the child's weight extremely well, plus it goes up to 45 lbs.
Full disclosure: I run a natural baby store called Babies Bottoms and More in Farmers Branch, TX and we carry Beco carriers (as well as a lot of other ones like Mobywrap, Baby K'tan, CatBirdBaby Pikkolo, and custom-made Mei Tais). You are more than welcome to come by and try them all on to make sure you pick the one you really want. Give us a call for hours and location, ###-###-####. :)