Personally I would have a single Google+ account for your business (with a link from both sites going to the same profile). You could then add each of your offices to Google Places as separate entities, to target the different areas.
You could list them on Google Places as:
<company name=""><street>, East Coast</street>
<state>,</state></company>
<company name=""><street>, West Coast
<state>,</state></street></company>
As far as what type of profile you choose I can't really comment on the differences between a local business page compared with a company page. To me 'Company, institution, or Organization' would be a single world-wide entity, whereas a 'Local Business or Place' would be a business with a single shop or a place of interest.
I would say that after a good 30 minutes of looking around on the Internet and Google help pages its a bit unclear as to what the difference is between the profile types, but I hope this helps.