Which cities offer the greatest opportunity/return for multi-family investment units

More than the city, I'd say it depends on your ability to find the right Seller (or lender) . . . ie, you could leverage that $150,000 as a 10% down payment into a $1.5M property and get a really nice return. Do understand though that the more you leverage the greater the downside risk, so be careful.
BUT, to answer your question, the best deals right now tend to be in the most destressed areas, which are South FL, Las Vegas, and Detroit. Demographics are working against Detroit (it's systematically shrinking over the last 30 years or so). So I'd vote for South FL or Las Vegas as they should continue to grow once the market rebounds. People don't want to retire in New Jersey you know.

I am a commercial real estate broker in SLC. The "quick and dirty" on SLC is that it is arguably one of the best multi-family markets for what I would call Capital Preservation. We are #1 in population growth, we have 3 major universities that put out a very large, young, educated workforce, we have an extremely diverse economy (so we don't see the dips like markets that have all their eggs in 1 basket). I have sold 130, 124, 43, 16, 32, 8, 8, 6, and close tomorrow on a 32 unit, and am going U/C on another 30 unit. Average unit pricing is about $68,000/door and climbing. Concessions have burned of and rents are expected to increase 3% to 6% over the next 12 months, vacancy is currently 5% and projected to dip below 3% inside of the next 24 months. Lots of reasons SLC is the place to be. $150,000 woudl likely only get you into a $600,000 property (25% down), but I have a 6 unit U/C currently at $550,000 that is a 7.5% CAP that with leverage would likley give you a 9% year 1 cash on cash return - and have very little downside and lots of reasons for future appreciation. In the biggest commercial recession since the Savings and Loan days in the early 80's our multi-family market dropped a total of 3% - and that coudl be argued to be a false reporting figure becase very little traded up until this year when debt became available again. Come spend your $ in slc w/ me.

I'd say where ever you are comfortable, but go for an actual cap rate of 14%,,,,,takes a lot of looking, make it in an area where you don't need a gun and dog to collect rents

As a commercial appraiser specializing in the multifamily sector for 20+ years, I recommend locations that are near Universities and Colleges, especially higher-prestige institutions (with students from more affluent families). Student housing is virtually immune from the typical up and down cycles (in vacancy rates, market rents, concessions, etc) that affect other apartment properties, at least here in Southern California.
Leases are for a full school year (August to August) and each unit is usually rented to a "tenant group," rather than to individual students. These leases are signed jointly and separately, typically with parental gauarantees. Therefore, individual student's comings, goings, or drop-outs have no effect on income - nor do summer vacations. The "tenant groups" (which may include fraternities and sororities as well as private party groups) in this area are expected to pay ALL utllities and also pay for any student-related damages.
Effective vacancy rates are zero and rents typically increase every year, no matter what the economy is doing. I recently appraised a 100+ year old USC frat house (with a newer attached fourplex) for the second time in six years, and the rents had increased by 36% from 2005 to 2011 - unheard of in the recent market. Long term appreciation is well above-average, plus many colleges have placement and/or management services to make things easier for landlords.
Look for buildings with a good unit-mix (lots of bedrooms) and avoid anything that is mostly Singles and/or 1BRs. Unlike standard apartment buildings, the price-per-bedroom is a key value factor here - 4 or 5 students per bedroom is not unusual. This sub-sector is a fairly well-kept secret, with such low risk and high gain - so you may have to dig a little deeper to find one - but they are the closest thing I've seen to a goldmine in the multifamily sector.

it also depends on how you structure the deal, in commecial there is nolimits nither regulatios, so if you use your omagimacion you can do a very good deal, but you need to know the cap rate of the area, and base on cap get to know what is the gross incom and operating expenses and run your numbers, do your DD, and you can negosiate as well.

For certian assets like credit tenat NNN properties I would be comfortable with the 48 states. However multifimily properties require some attention to work. I would pick an area that was at the most an hour drive from where you live, preferably not more than 30 minutes. With only 150,000.00 to invest you are a small investor and management can significantly degrade your return. I think you need to grow to at least 30 units to make some management work financially. You can get initial returns with growth if you pick the right area around 12-15%. The right area is not one where crime is high its one where the prices are depressed but the neighborhood is still good.
I would be happy to talk to you about tactics and strategy.
Tom Sullivan
Commercial Realty Advisors Inc.
tjs@comrealty.net

How does 20%+ return with no leverage sound? We are buying loans and properties from banks with ALL CASH and NO DEBT. That way, you don't lose your investment because a bank gets unreasonable and forecloses. Returns typically are 20% + annually (yes, it is possible... we just have to look hard and make a lot of insulting, lowball offers.). Our focus is in North Carolina. Great weather. Business friendly government. Jobs. Low prices. All the good stuff.
Here's to successful investing.

In your case I would say boring is better. In other words avoid markets suspect to large up and down swings (as there are many in this category now) and stick with more predictable markets that may not be first on the llist of a tourist destiniation but have a track record of consistency and profitability. There is a book you can get ahold of FREE that explain this process and what to look for as well.