Zulu, that's interesting. Just checked it out, and the tree is irrelevant. We live in West L.A. and the San Bernadino Mountains are to the east of us. Almost all of the transmitters are 45 to 48 degrees from us -- almost exactly North-East, toward the mountains (where as I recall from when I was a kid the transmitters are). There is a multi-story hotel down the street and one street over, but it is just about exactly due east, so the NE direction is not blocked; so too we have a big apt building down my street to more South East, so not in the way of NE. The houses across the street, two story, would block line of site from NE direction from my ground level. Not from my roof (as my house is kinda up on a hill from the houses across the street).
As an experiment, I moved our little TV up to the second floor and see if my old indoor antenae gets reception there. Still no luck using both the rabbit ears and the Terk antenae. It seems that digital signals are just more finicky than analogue for some reason, in terms of reception, and the digital signals from the NE/E direction are blocked. In light of this, I'm wondering if even a roof antenna would work, though the chart on that website seems to say one would (might). Maybe the big buildings around us are the source of the problem, though, as you suspected.
... Hmmmm ... I would like to get the Sci-Fi Channel and BET though ... Sounds like satelite and/or cable are my only options. Sheesh.