Where did Romans keep their liquid assets?

Mostly in a bank, the same as we do today.

Bankers in Ancient Rome were called nummularii or argentarii (among many other names with lots of overlap) and their system is rooted with the Ancient Greeks. They were private citizens who operated in city centers. There were also state-bankers called mensarii who occasionally also provided the same services as argentarii. The difference between all the names is confusing, as there is a lot of overlap and changes in the services of bankers over time.

Different types of bankers at times acted as:

• money changer (from foreign currency to Roman Imperial Mint coin; or from gold/silver/bronze coins into another; this is where bankers made most of their money by charging a fee just like contemporary airport currency exchanges)
• money lender (Carl has a farm and has never had any money problems. He goes to an auction and wants to buy an ox, so the banker settles the payment. Or Carl goes to the market to buy a leather thong but doesn't have the coin on him, so he has to borrow some money.)
• assayer (all coin payments were weighed and tested to make sure they were real coin, not counterfeit / filled with lead, etc. You may have been just paid your first gold coin and not know if it's real or not so you'd want to receive the payment at the bank, not by hand)
• minter (a select few bankers were sanctioned by the Roman government to mint and/or assay new coin)
• account manager / depositee (you set up an account where you can deposit your coin and the bank will also handle simple transactions for you)
• mediator (Bill and Bob both have accounts at the same bank. Bill wants to buy Bob's country villa, so they both go to the banker and set up a monthly payment contract on paper and transfer the villa with no real coin exchanged. This could also be mediated across vast distances through multiple banks.)

All bankers were sanctioned by the Roman government and needed to keep detailed records of everything they did.

Where did the bankers keep the physical coins? At first they followed the Greek example and stored them in temples, but soon started moving them to their privately owned storehouses.

There are plays that talk about banking and debt as a subject. For example Plautus' Epidicus (adopted from a Greek work) is a play about a father, a son, and a slave. The son borrows forty mince (coins) from a banker in order to buy a girl he has fallen in love with. It also has some real Oedipus-level plot twist in it.

Fun fact: the word for bank in many languages is the same as the word bench, or has a common root with the word table. That's because bankers would sit at a long bench (bancu) or table (Greek bankers were called trapezitoe) in the middle of the market, so that people could borrow money or change money. The banker was like the marketplace's cash register / till.

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA%2a/Argentarii.html

Banking and Business in the Roman World, Jean Andreau, 1999

The ancient Roman playwright Plautus wrote a play entitled "The Pot of Gold" in which an old miser discovers, through the help of his household spirit, a pot of gold buried in the house by a previous occupant. Much of plot revolves around his efforts to safeguard his pot of gold and slaves' efforts to steal it (the play is incomplete).

I'm not sure how enlightening this is for you, but a cache of gold coins buried inside a house must have been typical enough for the audience to relate to the play.

here's a bit from the New York Fed on the Roman economy that's well annotated.

the short answer is that people by and large did not hoard coins -- Romans had access to simple banking, credit, insurance, and a bevy of financial devices many of us would conceitedly consider to be modern. the history of credit is very, very old of course -- it's coinage that's more rare and strange in human history, actually -- and it doesn't progress much from era to era. we would, for example, consider mortgage-backed securities to be new, and to some extent they are novel -- but mortgage debt (and other notes backed by good credit) was certainly transferable in the ancient economy and used as a liquid asset. as Paul Volcker pithily noted (and we have to paraphrase), the only innovation of any real value in finance in recent times is the ATM.

it is very likely that, then as now, financial crises were the product of the vacillating expansions and contractions of the massive private credit complex that dominated their economy.

of course, the Roman world went far beyond Rome and there were places -- notably if you were a paid Roman solider -- where one actually did hoard coins, even if the hoard did not represent the entirety of one's wealth. that we stumble over hoards with metal detectors every now and again is testament to that. but one shouldn't consider that to have been normal.