But my accountant tried to dissuade me from doing it...
As a real estate investor (not an attorney or tax professional), your accountant's reaction strikes me as a little odd. Does he/she have much experience with real estate?
1) LLC =/= different tax filing. Your LLC can be taxed as a pass-through, S corp or C corp; that your accountant would not discuss the pros/cons of those tax options would concern me.
2) Fees vary widely by location. In my area, they are $50/year.
3) This comment was referring to "piercing the corporate veil". Keep a separate checking account for the property that only that property's income and expenses go through. Make sure to sign any paperwork as "Mr. Gentmach, Co-owner Building LLC" instead of just "Mr. Gentmach". If this is your first rodeo, an hour with a recommended real estate attorney in your area may be a good investment for a checklist of do's and don't's around this but really, it's not complicated.