@Susie C.
Some thoughts:
1) it really depends on what your long term goals are. If you want to build a large portfolio vs own a few properties.
2) I don't invest in CA and have actually never been in the state, but judging by all the reading I've done here on BP about SF and the Bay Area it seems very difficult to plan on building a large portfolio there based off of investing there due to such high purchase prices and in many cases low to even negative cash flows. Basically this asks the question, if you are investing for cash flow there, then how long will it take you to reach your goals?
3) I can't speak for other areas of CA obviously as I stated above having not yet even so much as visited the state - BUT - that same money you are talking about for a down payment on one property in SF could be used in many many other parts of the country to buy handfuls of property or decent sized apartment complexes (20-40 units), which very seriously will produce returns high enough to pay for that 2000$/mo mortgage and then some. So you can buy there and spend it all on a down payment for one property OR you can buy outright or leverage that same amount of money to own many many properties in another part of the country, creating equity in those properties and making enough to easily pay that mortgage in SF AND having money left over as well.
4) to give an analogy this sounds like - you are hungry and have one seed to plant at the moment. If you plant the seed you have two choices 1) grow the plant and harvest more seeds which you can plant and then eat as well as harvest and plant more seeds OR 2) grow the plant and eat it and be out of seeds with little to no means to have any in the future.
If you want more than just a couple of properties in your lifetime then perhaps a long review of your options would be the most prudent choice to make if you have access to 200-250k. That buys a lot of property in other areas of the country and produces far more than the equity pay down on an 800k house/condo. I'm sure you can find someone to disagree with me but if I had 200-250k I would not park it in a 20% down payment situation when I could use it to multiply that amount elsewhere.
AND - why would you want to spend 200k as down payment on a 1M property just to turn around and still have to rent a bedroom out and have to live with someone else in YOUR home??? Very few people would be willing to make that deal.