siteboundary=None
for lyr in QgsMapLayerRegistry.instance().mapLayers().values():
    if lyr.name() == "@@@@@":
        layer 1 = lyr
        break

targetlayer=None
for lyr2 in QgsMapLayerRegistry.instance().mapLayers().values():
    if lyr2.name() == "@@@@2":
        targetlayer = lyr2
        break

siteboundaryshapes = siteboundary.getFeatures()
targetlayershapes = targetlayer.getFeatures()

for count,i in enumerate(siteboundaryshapes):
    siteboundarygeom = i.geometry()
    siteboundarybuffer = siteboundarygeom.buffer(1000,25)
    siteboundaryatt = i.attributes()
    print (siteboundaryatt[1])

    for j in targetlayershapes:
        targetlayergeom = j.geometry()
        targetlayeratt = j.attributes()

    if targetlayergeom.intersects(siteboundarybuffer):
        print (targetlayeratt[1])
    else:
        continue

layer 1 feature 1 attribute

layer 1 feature 2 attribute
layer 2 feature 1 attrbute
layer 2 feature 2 attribute

layer 1 feature 3 attribute
layer 2 feature 1 attribute

layer 1 feature 4 attribute
layer 2 feature 1 attribute

etc etc

layer 1 feature 20 attribute

from qgis.core import *
import processing


layer1 = processing.getObject('ne_10m_populated_places')
layer2 = processing.getObject('ne_10m_admin_0_countries')

all_features = {}
index = QgsSpatialIndex() # Spatial index
for ft in layer1.getFeatures():
    index.insertFeature(ft)
    all_features[ft.id()] = ft

selection = [] # This list stores the features which contains at least one point
features = layer2.getFeatures()
for feat in features:
    inGeom = feat.geometry().buffer(1000,25)
    idsList = index.intersects(inGeom.boundingBox())
    #print "found %d points"%len(idsList)
    for id in idsList:
        testGeom = all_features[id].geometry()
        testGeomP = testGeom.asPoint()
        #print testGeomP.x(),testGeomP.y()
        if inGeom.intersects(testGeomP):
            if feat not in selection:
                selection.append( all_features[id])
            else:
                pass


# Select all the polygon features which contains at least one point
layer1.setSelectedFeatures([k.id() for k in selection])