Just about any "modern" 8-bit SRAM chip can be used to substitute for these, with the understanding that the pinout will be different and you'll need fewer of them. There are inexpensive 2Kx8 devices which will substitute nicely for up to four 1Kx4 originals, and 8Kx8 devices that will substitute for as many as sixteen.
In general this will also obviate the need for some decoding circuitry. In the SYM-1 specifically, there's a 74LS138 interposed between the 3-NOR gate detecting the bottom 8K of address space, and the four pairs of 2114 SRAM sockets; the four lower outputs of the '138 drive
/CS of one pair of sockets each, while the others appear to lead only to the expansion connector. A single 6264 SRAM (8Kx8) could replace both the 74LS138 and the eight socketed 2114, to provide twice the usable RAM of the standard configuration. It should be straightforward to build a one or two-layer PCB daughtercard which plugs into the original sockets to obtain all the necessary signal lines to lead them to a 6264.
Any surplus address or data lines can be tied high or low - directly for address lines, through a 1K resistor for data. The original devices do not have
/OE pins, so these can simply be tied to the
/CS pins (same function, just different possible names) on the replacements. If there is an active-high
CE2 (as on the 6264), tie it high.
Power consumption on modern CMOS SRAM devices is negligible, compared to the rest of a predominantly NMOS/LSTTL based system.