Help to choose caps for noise filtering
The 5V switching power supply has no datasheet but there is information on the web page that says its ripple specification is measured with 10µF // 100nF, so we can safely assume it will be stable and work fine with this amount of capacitance. 

They don't say what type of cap is is, but I will assume ceramic since a 10µF electrolytic would have several tens of ohms ESR and be completely useless at ripple filtering anyway.

More capacitance (like your 470µF) will most likely work. A 10µF 16V X7R SMD ceramic cap should work fine too. It will also filter ripple better than an electrolytic due to very low ESR and inductance. If you use a 10µF MLCC it is unnecessary to put a 100nF cap in parallel. You can always put the footprints for both electrolytic and ceramic, and use the one that gives lowest ripple (check with a scope).

The caps at the output of the AMS1117 are another matter, for this you should look at the 1117's datasheet. The 100nF cap at the output is most likely redundant, as there will be at least one ceramic cap on the ESP8266 module PCB, so you can remove it. Ceramic caps have low ESR, so by putting 2 ceramic caps in parallel, with a length of trace or a connector in between acting as an inductor, you risk creating a tuned LC circuit which can resonate.

Now the datasheet says:


  The circuit design used in the AMS1117 series requires the use of
  an output capacitor as part of the device frequency compensation.
  The addition of 22µF solid tantalum on the output will ensure
  stability for all operating conditions.
  When the adjustment terminal is bypassed with a capacitor to
  improve the ripple rejection, the requirement for an output
  capacitor increases. The value of 22µF tantalum covers all cases of
  bypassing the adjustment terminal. Without bypassing the
  adjustment terminal smaller capacitors can be used with equally
  good results. 


They don't mention ESR, which is annoying, but solid tantalum caps will have ESR around "one to a few ohms", so you can aim for that. You can also use an aluminium electrolytic cap, if it is a general purpose one you'll need a lot more µF to get the ESR down. The 470µF cap you planned to put on the input of the LDO should work just fine on the output, if you already have it, no need to pay extra for a tantalum.

A similar regulator datasheet says:


  The TLV1117 device is designed to be stable with tantalum and aluminum electrolytic output capacitors having an ESR between 0.2 Ω and 10 Ω.


Also make sure your LDO is properly cooled! Calculate dissipation and  leave enough copper area on the board, connected to the LDO's tab, to suck out the heat.