I don't think you can avoid it. Even if you don't state your experience, you'll have to provide an answer when asked. I'd start thinking of ways to creatively frame your downtime. Employers like hearing that, if you weren't getting paid, at least you were motivated to better yourself in some way. Motivated employees are productive employees.
Doubly so when you have no real work experience to fall back on. When an employer sees you don't have a lot of tangible work experience, period, they ask themselves "Are we gaining or losing value by hiring this person that will have to be invested in to be successful?" If you present yourself as eager to learn, self-motivated, capable of figuring things out on your own....that makes you a far more attractive prospect, regardless of your work experience. It's just, when you have no work experience, personality is THE thing that sells you to an employer.
In many cases, that means lying to an employer about who you really are in your downtime. If you turn out to be a fit for the company, it gets overlooked. If you turn out not be a fit....it's seen for the lie it is. In this economy though, I'd say go for it. Just getting your foot in the door is its own thing, you can worry about living up to the expectations you set if you actually get hired.
In any event, don't fall back on any old activity in an attempt to pad your resume. Things like "I volunteer at the animal shelter" and "I write a freelance column on video games in my free time" is white noise to an employer unless it's germane to the job you're applying for. Now, stuff that's of note, like volunteering at prestigious places or for really important work, that can be an asset when applying. It depends in large part on the kind of company you're applying to. Large businesses have a different culture than smaller one, which are both culturally different than full blown corporations. Franchises value different things than Mom & Pop establishments, ect...
As someone that has talked their way into plenty of jobs, I can just say: eye contact, honesty and assertiveness have gotten me hired where my resume/application/work history wouldn't have.