Much of the time it is not less expensive to live in an RV overall than to rent an apartment. I won't go so far as to say that this is always the case, but RV living is not particularly inexpensive. RVs are not as energy efficient as houses or apartment buildings overall (particularly in relation to heating and cooling, due to comparatively poor insulation), though their small size can partly make up for some of that.
"Is it common to find places to park for a month or two, that are reasonably inexpensive, close-by to major cities?" I suppose the answer would depend on what you mean by "reasonably inexpensive," but I suspect generally the answer would be "no." Most campgrounds that have monthly rates are at least a few hundred dollars a month, and ones close to big cities are usually more expensive than ones out in the boonies.
Most if not all long-term parking/storage lots would not permit living in the RV. Many short-term parking lots also don't permit living in the RV, for that matter. Many housing developments and neighborhoods have restrictions on parking RVs, so often crashing at a friend's house for a month is not permitted even if the friend does not mind.
As Don mentioned, fast and reliable internet access in campgrounds is quite rare, and providing your own (via a cell phone or whatever) often gets quite expensive.
