First off: EXCELLENT savings rate. You'll be to FI / ER in no time if you keep up the low cost lifestyle and saving / investing such a high fraction of your income.
What others said on the high deductible insurance. Cover your arse.
You have PLENTY in your savings / emergency account. 6 months = 6 * 760 / month spending = 4560. Double that to be conservative, then round off to a nice even 10k. You state you have 29,800 in the ING Savings and another 4,500 in a "rainy day" account - that's a combined 34,300. That leaves about 24k for other uses besides being emergency / rainy day.
What is your time frame on that place you want to buy? 6 months, 12 months, 2 years, 5 years? If you have plenty of time, then don't sweat it in the short term. No matter what, DO NOT use all your savings for a down payment. Owning means, if anything, you should have more saved up for the post purchase rainy day fund. That 10k noted above will need to be factored up, most likely, to cover 6-12 months of the mortgage, which will probably be more than your current $270 in rent. Also factor in maintenance surprises. If you're buying an "apartment" (condo for everyone outside of NY) watch out for the assessments for building / complex level repairs. Factor in the monthly maintenance fees and taxes and home owners insurance over and above the principal and interest payment on a mortgage - some places can really ream you on these other costs. And recall, in any socialized ownership structure (condo, NY style apartment, etc) you have to deal with neighbors on the board - some are financial idiots, who will delay small maintenance issues out of being cheapskates, resulting in huge repair bills / assessments later instead of small or modest ones today. Others could be grandiose consumers - spending way more than necessary on fluff, and sticking you (as one of the owners) with the bill. Pick you building / condo carefully (I personally wouldn't choose a condo / apartment for those reasons alone - YMMV, different strokes for different folks, etc).
Also a bit of note on your terminology: "Savings" and "retirement account" are both forms of capital accumulation. One, in the common lexicon, a "savings account" is just more liquid and with FDIC insurance and on average lower returns in today's ZIRP environment than the other which may also have some tax advantages. Excess income over spending, no matter what you do with it immediately (put it in a "savings" account, retirement account (401k, 403b, Roth IRA, Traditional IRA, etc), a taxable investment account (with stocks, bonds, money market funds, tax free bonds, ETF's, mutual funds, etc), cash under the mattress, etc) is SAVINGS - its just that some forms are more immediately liquid and have different potential tax implications.
Are you putting in enough on your contributions to get the maximum company match? If not, you're leaving "free" money on the table. Increase the 403b allocation of your savings (e.g. income over expenses) if / as required to take full advantage of the match if you're not getting everything you can from the employer.
Re the car: Once you ditch the lease, you already have enough cash on hand to replace. See above where you have 24k more than needed for a rainy day account. That said, the longer you delay, the better you'll be. I presume that $290 INCLUDES car insurance? If not, be sure to price out what it'll cost if / when you buy a cheap used car in cash. Also, Financial Samurai suggests that a car shouldn't be more than 10% of your annual income - so using his rule of thumb, keep it to ~3,500 for the used ride.
