Cliffs Edge is nice. I also love Il Capriccio on Vermont. Very reasonably priced and you bring your own wine. No corkage fee.
Also, Dusty's on Sunset in Silverlake. Yummy French.
Michaelangelo's is still pretty good and not terribly expensive.
We love Blairs, but that might be too expensive for your needs.
How moderate? How close to Echo Park?
My first thoughts would be, I think, that Beaujolais (really eagle Rock) Aroma (Silverlake/Echo Park) and Cappricio (Los Feliz/Vermont) fill the bill, more or less. But you KNOW about them. Haven't been to Michaelangelo in close to a decade. If you're looking to be REALLY bargain-minded, there's always Taix...
I don't know of anything much newer....