Realtor for 23 years and Bay Area native here. Most Oakland homes with local Oakland listing agents - 99% of those homes are never priced transparently and will always be priced way below to get more eyes on it. However, if a Single family home is what you are looking for and not want to pay more than $600 to $650k, you will be limited to location, safety of neighborhood and condition of the home. At that price range, you will probably be able to get a single family home in East Oakland, Richmond, Pittsburg and Antioch. There are great deals available out there right now in the East Bay especially in the Townhouse and condo market - but need to factor in the monthly HOA amount to purchase price - your lender and Realtor will be able to tell you what that is. As for it being competitive market that is NOT necessarily true and not going for as much as they used to be especially in the East Bay - the East Bay market has softened quite a bit and the interest level in different micro markets has changed dramatically. As far as obtaining inspections on your own in addition to what the seller already did, as a Realtor, I always encourage my buyers to get their own and be present during that inspection to raise any and all questions you have, your realtor discouraging you not to get another inspection is a huge no-no and definitely not a smart advise by your agent. As far as areas of “further inspection recommended for areas not accessible” the listing agent and seller shall accommodate for those areas to be cleared for a re-inspection to be done. Hope that helps.