What can I replace a BSS138 N-Channel MOSFET with?
See here -> Digikey has the BSS138  and they can be obtained from them relatively quickly.
 They do not seem to have through hole versions.
Once you play a little you will find that the SOT23 smd pkg is not too hard to hand solder - and you can add wire leads if needed. 

That level shifter circuit is trickier and more critical of part characteristics than most simple circuits are.
The BSS138 is an "N Channel MOSFFET". It has a much lower turn on voltage (Vgson) than most similar MOSFETs and this is important in this circuit.  

Alternative parts in through hole are available but they are less liable to be available to you than a BSS138.  eg see Digikey for TN0702 or maybe the  LP0701 - but BSS138 is available from the same supplier. If you can learn to handle the SOT23 pkg a lot more parts will be usable.