Most resources around the Internet discuss common antenna types, classifying them between directive (like Yagi) and nondirective (like a simple dipole). Directive antennas are good when you know from which direction you are receiving a signal and would like to collect as much of it as possible. Nondirective antennas are good when you do not know from where you are receiving, or you want to receive from many directions at once without moving your antenna.
I would like to build a weakly directive antenna: i.e., I don't know the direction from which I will be receiving, but I know it must be in a certain half plane or quadrant around my position (because in the other directions there are buildings that screen any interesting signal, and unfortunately I do not have easy access to an unobstructed position).
I could use a nondirective antenna that also listens in the useless directions, but maybe I can squeeze some dB more if I can exclude them. What are good antenna types for this kind of application? Pointers to designing resources are welcome!
EDIT As specified in the comments, my band of interest for this antenna in VHF/UHF. Mostly UHF, actually. I am looking for antennas whose radiation pattern is something like one of these two pictures.
I would consider an antenna nondirective when it has a radiation pattern more or less like a circle, and strongly directive when the radiation pattern is a circle sector with a small angle (and therefore a strong gain in that sector), like 10 degrees or less. Since this is intermediate between the two extremes, I would consider this weakly directive, but if this is non standard terminology just ignore it.