Recently, I got a 3D printer, (https://www.monoprice.com/product?p_id=15365) and it has been a blast, but I am running out of ideas of things to print, I like doing mechanical things, with gears and moving parts, and puzzles, but I need more ideas of things to print. Any ideas appreciated.

Make your own slide case for a CE.
https://www.thingiverse.com/thing:2057914

I saw that, but my print bed is only 120mm by 120mm, so it won't fit!

Is it possible to print out different pieces of it and glue them together? I'd print rockets, or planes. Or a calculator slide-on case that encloses the main body. (same as the other case )

It is possible to do that! There are even some special glues for ABS plastics that make the bond particularly strong. Take a look at some of the projects geekboy and I worked on for our Da Vinci 3D printers.

I use PLA plastic, because it is the cheapest, it is easiest to use, and it doesn't smell bad when melted, but I was thinking of modifying the design thelastmilennial suggested and printing it in two pieces, then snapping them together.

How tall can your printer print? I've started designing an entirely 3D printable model rocket in Onshape.
I printed these with a .4mm nozzle and .2 mm layer height

Each of the cylinders and the nose cone are printed in 1 layer thin vase mode with no top or bottom fill. The casing mounting brackets are printed with no top or bottom but infill of 30%, and .4mm outer walls
The fins are printed with .4mm outer walls and 10% infill with yes top and bottom
The launch lug is the same as the fins.

if you know how to use Onshape you might be able to adjust the height of the body pieces to fit your printer.

My printer can do 120mm by 120mm by 120mm. I have never used Onshape, but am very familiar with Creo parametric.

so, it looks like if you wanted to print this rocket you'd have to shrink down the outer body tube to 4" tall instead of 5 and also probably the nose cone. You'll probably also have to shrink the fins and the engine housing, but it's still doable for you. the one I linked to you is sized for a D estes engine. Probably just edit the extrude features to be 4" tall and print out a lot of body pieces and couplers. You also need two of the engine casing mounts.

just found this: https://gigdigit.com/extended-heat-bed-kits-120-x-250mm-print-area-3mm-thick-select-mini-v1-v2/ online, and now I want to so bad! too bad it's $85

Build a house

https://www.telegraph.co.uk/technology/2017/03/03/incredibly-cheap-house-3d-printed-just-24-hours

Mod note: antisemitism will not be tolerated

*edit
Sorry about that it wasn't meant in harm actually one of my best friends is Jewish, I was only messin around, soz lol
Just to be clear he is actually Jewish

If only we had a manufacturing process for conforming plastic to a certain contour or shape that would allow us to produce these plastic houses much faster then using a 3D printer

Oh this is a perfect idea! Print a Curta calculator! It's a mechanical calculator with tons of moving parts. It's also a bit of a puzzle to put together. You can download the parts (for free) here. You should also search videos about it on YouTube, it's awesome to see how it works and it's history!