The first thing I would suggest (at a bare minimum) would be to have an extra propane tank on hand at all times and when one is empty make sure it gets filled right away. They have a tendency to get thrown in the garage and people usually forget to fill it up until both tanks are empty. On a job a few years ago we discovered an easy solution to this age-old problem and it was as simple as hooking up the gas grill directly to the home's natural gas piping. Don't get me wrong, I am not saying it was simple nor do I recommend you attempt to do it yourself because any work on gas piping should be performed by a professional (plumber). We work with several of the area's best plumbers so feel free to ask if you need their names.
When purchasing a new grill you might have the option of getting it set up for propane OR natural gas so you first need to determine the fuel source. Propane is more common in rural areas with limited natural gas underground piping and propane has twice the amount of BTU's per unit at natural gas. But with natural gas being about 1/6 the cost even with the efficiency being half of what propane is, you still end up spending about a 1/3 what propane would cost. With the small amount of gas you use I think convenience is what you are really paying for, especially since you will need to pay for the plumber to do the piping. If you already have a grill and need to switch over to a different fuel then you will need to see if you can get a conversion kit from the grill store. Otherwise you might need to upgrade your grill. Another thing your plumber will hopefully check is the regulator which adjusts how much pressure the gas will be under when it arrives at your grill. Too much or too little and it'll likely not work correctly. The gas pipes will need to be sized properly with a shut-off near the grill or where it exits the house and I would also suggest installing a Quick Disconnect fitting so you can easily remove the pipe without the need for any wrenches. There will need a flexible hose coming off the hard pipe exiting the house so the grill can be shifted without disturbing the fittings and causing a gas leak.
A common trend I am seeing is for folks to install outdoor kitchens on their property and with good planning this can be an amazing space for your family to enjoy during the warmer months. Even during the cooler months the space can be outfitted with those upright patio heaters you see at restaurants in California.
After I installed several of these hook-ups for our clients I decided to switch over to a charcoal grill which I have not regretted one bit. As much as I like the speed an convenience of gas, the smell and taste of meat cooked on charcoal is so much better, especially with wood chips thrown on for good measure.