i don't know how clever it is but here's how i do it:
E2 and SN2 are both dependent upon the rate of the base/nucleophile hence the 2 (for second order kinetics I think). So a strong base/nucleophile is indicative of E2 or Sn2.
Weak base and nuc. is Sn1 or E1.
#2 is a backside attack - (like having to go to the bathroom number 2 is an attack of the backside) so, a strong but bulky base cannot make the backside attack due to steric hindrance so you have only E2.
generally any base with a negative charge is going to be 2nd order - so then you just have to watch for the bulky ones like tertbutyloxide to determine if it is a mixture of SN2 and E2 or just E2.
other than that i don't know any good tricks - just memorize the substrates/alkyl halide types and which reaction can take place then apply the rules above about strength of base/nucleophile and you should be in business.