Mount subpanel on below grade stem wall
Immediately to the right is the best place for the subpanel

If I were you, instead of using either location #1 or location #2 marked in your picture, I would position the subpanel in the bay immediately to the right of the main panel, provided it is a full-sized (i.e. 14.25" wide) bay, of course.  This allows it to share the 30" width of required clear working space with the main panel, keeps the subpanel panel clear of minor flooding, and allows the nipple fill and derate rules to be used for the feeder, saving cost.  It also accommodates the desire to expand the window to the left, albeit at the cost of removing the insulation batt and temporary support jack that have already been fitted to that right-hand bay.

Your panel-alcove will need to be 30" wide, and clear from floor to ceiling

Since you are building a wall out from the existing basement wall, and the NEC 110.26(A) clear working space extends out from the front surface of the hardware in question (i.e. the existing panel), you will need an alcove that is a minimum of 30" wide and provides enough space for the doors on both the existing and new panels to open 90&deg;.  Note that while this alcove need not be centered on the existing or new panels (and it won't be, in order to accommodate both of them in the same niche), it will need to extend floor-to-ceiling, due to the height requirements in 110.26(A)(3).

As to specifying the subpanel itself...

Given that your existing main panel is an Eaton CH, you are going to be limited to a 125A subpanel/feeder by the fact that the CH line lacks breakers upwards of 125A (CH2150s and 2200s used to exist, but were discontinued a while ago).  As a result of this, and the fact there is no 30-space, 125A rated, main lug or convertible loadcenter in the Eaton CH line, we have a choice -- either you can go with the Eaton CHP24L125X2 (less costly, but shorts you on spaces), or the Eaton CHP32L150X5 (costlier and harder to find).

For either choice of subpanel, you'll want a CH2125 for the main panel to serve as your feeder breaker, along with a 1.5" RMC nipple of appropriate length, a tensile-capable stud shoe such as the Simpson HSS2-SDS1.5 with its full complement of specified fasteners, 3' of 1/0 Al XHHW-2 to connect the feeder breaker to the subpanel, and a NL20 neutral lug for the main panel to connect the feeder neutral to, as well as minor parts such as locknuts and fasteners, and some THHN and wirenuts of the appropriate size to pigtail the wiring for the displaced breaker over to its new home.

...and installing it

The nipple will go through a bored hole centered widthwise in the existing stud, with the stud shoe over the top of the bore to reinforce it, as per the 60% rule for reinforced bores in IRC R602.6, which allows a 2.1" bore vs the 1.9" OD of a 1.5" nominal rigid metal conduit.  Furthermore, this hole will be located and the nipple placed to connect the bottom KO on the right side of the existing panel to the bottom KO on the left side of the new panel, as these KOs are 1.5" at their smallest, and our rigid nipple provides both a grounding connection from the new panel back to the old and 800mm2 of fill for inter-panel wiring as per the 60% nipple fill rule in the NEC, which is ample space for both the feeder wires (at just over 300mm2) and all 24 branch circuits fed from the new panel, if need be (at just over 400mm2, assuming they are all individual 20A branch circuits and they are all being moved over from the main panel). Furthermore, you'll want to invert the new panel's interior when it is installed so that the main lugs sit at the bottom (this will make wiring easier).

Once we have the conduit and new panel installed, then we can move onto the feeder breaker and wires.  You will first need to take the wires off of a 2 pole breaker or adjacent pair of one pole breakers (as well as any matching neutrals), transplant those breakers into the new subpanel, and run THHN pigtails through the nipple from the old breaker's new home to the existing wiring, making the connection in the old breaker panel using the wirenuts, since it appears your existing panel is a 32-space unit that is full to the brim.

Once you have space free for the feeder breaker, you will then install it into the main panel along with the feeder neutral lug, and then run the fat aluminum wires from the feeder breaker and neutral lug in the main panel to the appropriate main lugs in the subpanel.  You will need to ensure that all connections here are torqued to manufacturer specifications, as well, with am inch-pound torque wrench or torque screwdriver.  This is a new Code requirement, found in Section 110.14(D) of the 2017 NEC, and also important to keep your electrical system from pulling a Greg Biffle on you.