A 1000 watt hair dryer is a huge load on a couple of batteries, even if its only on for 10 minutes that's about 17 amp hours or roughly 20% of your useful battery capacity assuming you have 200 amphours (you should only take batteries down by about 50%). The coffee maker will be something similar. You'll find that you will be running the generator to recharge anyway.
Why not just heat water for coffee on the stove while boondocking? I put coffee of my choice in empty teabags and do it that way, others use a french press, others a single cup dripper. The hair dryer is another story, but is that really necessary while boondocking?
If you really want to install an inverter then get at least a 1500 watt one, preferably 2kw (they perform better and last longer when not run at full power. Get a true sine wave one, not a "modified
sine wave" which is really a modified square wave.
Yes, you could install it under the bed, and do put it as close to the batteries as possible. You will be pulling upwards of 150A so you'll want to use a minimum of 1/0 cable. That is big cable, so shorter is better. Also, don't connect directly to the battery, place a 150A fuse at the battery positive terminal to protect that circuit. The other consideration is heat, inverters are roughly 80% efficient, which means that about 20% goes to heat the area around the inverter. That is a couple of hundred watts in your case. So, you will need some good ventilation under there.