Like others, I'll boot-up at the car if parked near slopes. Otherwise, carry stuff into base lodge in old boot bag, boot-up and leave bag in free cubbie. If no free cubbie, I'll throw bag in corner and/or under table, or on top of pay lockers. It's been about 25 years since I rented a day-locker. Carry valuables on my person. If I'm brown bagging my lunch, sometimes I'll bring the boot bag up to a mid-mtn lodge and return to it at meal time or if changing clothes.
Where are you planning to do most of your skiing? Generally, Eastern US and all over Canada ski areas are set up better for booting-up in lodges and stowing bags there.
Base lodges are less user friendly or barely existent at many larger ski areas in the west. But there are some good places out there for boot-up and free stowage, for example:
Alta: Gold Miner Daughter's café on the ground level facing the lifts, indoor cubbies.
Jackson Hole: Nick Wilson's Cowboy Café under the tram building, facing uphill, indoor stowage available under benches in dining area.
Lake Louise: large, free cubbie area in the magnificent base lodge, towards looker's left of complex.
Snowbird: there is a brown bagger room in Snowbird Center (base lodge) and there is an atrium nearby where it is easy to find a place to stow your bag. There is a scenic brown bagger room on the ground level beside the Mid-Gad Restaurant, this is a good mid-mtn place to stow bags and/or eat DIY meals.