"Think how this food would taste"
Here are some other non-specific words that might be useful. I started the trail by searching for synonyms of imagine and then selecting non-visual ones.
"pertaining to mental conception," 1820 (there is an isolated use from 1662), from Medieval Latin conceptualis, from Latin conceptus "a collecting, gathering, conceiving," past participle of concipere "to take in" (see conceive).
late 14c., "to represent" (in painting or sculpture), "make a likeness," also "to have a certain shape or appearance," from Old French figurer, from Latin figurare "to form, shape" (from PIE root *dheigh- "to form, build").
late 14c., "to fix the mind upon for careful examination, meditate upon,"
Meaning "take into the mind, form a correct notion of" is from mid-14c., that of "form as a general notion in the mind" is from late 14c., figurative senses also found in the Old French and Latin words. Related: Conceived; conceiving.
c. 1300, gessen "to infer from observation, perceive, find out; form an opinion, judge, decide, discern;
A few more: anticipate, conjecture, speculate, surmise, suspect, entertain, ponder.
All the above derivations are from etymonline.com - I gave them to show that the words did not specifically originate from ideas of "sight".
I may return to this list if any more occur to me.