Hello Synthia,
I think you are off to a good start in thinking about a place to buy. You should be able to find something decent for $225,000. Alas, it may not be in Alki. The only places I've been seeing in Alki are studios that are less than 500 square feet, and that may not be ideal if you have two large dogs.
If you've been prequalified for $225,000, you may want to set your home search parameters up to $250,000. There are homes/condos that have been on the market a while and so now it wouldn't be unreasonable to make a lower offer on something that hasn't sold at that price. Sellers will either accept/counter or they won't.
When shopping for a condo, please keep in mind the Homeowner's Dues, which, for a 1-bedroom can run from $150.00 per month and up; for two bedrooms, dues usually run between $200 and $300 per month on top of your mortgage, and can even go up to $400. That means your condo purchase would have to be around $200,000, roughly, to stay within your limits.
As for condos w/patios for large dogs - There are a couple on the market...but you must check with the condo association to see if they allow large pets. There's a complex right next to Westwood Village, MLS #28068502, that is listed at $225,000 and is a 2 bed/1 bath. Homeowner's Dues(HOD's) are $179 per month.
I would also try the WestWater, a new condo conversion located at 6960 California Ave SW, right by Caffe Ladro and south of the Morgan Junction. These have been on the market a while, and start in the low 200's. They are hot to get these sold, so I imagine there's bargaining room.
If you like waterfront living, have you considered Des Moines? It's a short 10-15 min drive from W.Seattle, on the "secret" highway 509, and there is a wonderful waterfront community there that is facing some new development and growth. MLS#28088907 is a 1bed/1 bath condo at Whaler's Village, which is right on the water, priced right at $160,000. There are a few other condos available in the downtown Des Moines area, several located in the Spyglass condos at 21937 7th Ave S.
I would also love to plug my area, which is Burien!! We have some good buys over here, and Burien is a very nice place to live. I grew up in W. Seattle but am perfectly happy here in B-town. There are a couple of new condo conversions, one at 615 Ambaum Blvd SW, which is the quiet part of Ambaum just a few blocks from up & coming downtown Burien; and one called City's Edge that's also just past SW 116th ST on Ambaum. Both appear to have grassy common areas, and both have been extensively remodeled and are very nice. But remember to check w/the homeowner's association in regards to the dogs...
Good luck out there! And in answer to your question about realtor referrals, I'm not going to beat around the bush...I would like to refer...myself!:) - Mon May 26 2008, 14:40