Does NMDA-receptor activation depend on neighboring AMPA-receptor activity?
Yes, there most certainly is "local membrane potential".  There are two major levels of compartmentalization in dendritic processing.  For one, most excitatory synapses occur onto "spines", which have a somewhat segregated environment from the rest of the dendrite.  The spine neck has been estimated to have a resistance of up to 1GOhm, although measurements are very difficult, so discussion spans orders of magnitude.  The other level of compartmentalization is that different dendritic branches can function somewhat independently.  

It is actually extremely important that there be "local membrane potential" and that AMPA receptors only activate neighboring NMDA receptors.  That is because Ca2+ coming through NMDA receptors leads (through many steps) to LTP (long-term potentiation) at that synapse.  We want LTP to be synapse-specific (only the activated synapse should be strengthened).  This requires that NMDA currents be specific to the synapse that had the AMPA current.  

Wikipedia has an excellent article on this subject: https://en.wikipedia.org/wiki/Dendritic_spine.  See especially "Modeling spine calcium transients" for discussion of the extent to which NMDA mediated Ca2+ transients are local.