The stock markets are, mostly, in physical locations. The NASDAQ is an example of a market that is entirely virtual. Nonetheless, that has no relevance to your situation with only $10,000. If you wanted to trade on the NYSE you would have to buy a seat on the exchange. That would cost you several million dollars.
What you want to do is open a discount brokerage account. If you are in the US, then E*Trade, TD Ameritrade, or Charles Schwab will work well. Day trading is ill-advised even if you were experienced for several reasons.
First, the trades do not appear on the tape in the order in which they happen, always. In fact, the daily high and low are not the true high or low either. Large orders are taken "off the tape," and are reinserted in whole or in part during the day at such time as the broker-dealer handling the transaction at the weighted average price. People who think they are day trading and seeing this really big signal can be responding to transactions that happened much earlier in the day.
To give a personal example, I entered an order that cleared at a price above the market high. In theory, that should have meant that my order was the highest priced order for the day and the high should have matched my price. My order appeared on the tape at a lower price than I paid because it was averaged in with other orders as part of a block trade and didn't report til later. I only know this because when I realized the price that my order cleared at, I was going to take a screenshot and frame it. Unfortunately, the trade never made the tape and market high price was fifty cents lower per share than what I paid. I have never been the high or low before. I did once buy a major firm at 1/8th above the firm's all-time low price, but that isn't the same as paying the all-time low price. That was a long time ago because we stopped trading in 1/8ths in 2001.
The second reason is that you haven't yet learned the rules. If you had, you wouldn't be trying to day trade.
For you, the stock market happens wherever you have your computer. Open a discount brokerage account. Your better bet is to learn to buy securities under a rule that you cannot look at your computer more than once every second Wednesday. A lot can happen between two Wednesdays that will be out of your control. If your trades can survive your absence, you will do fine. If you have to look at it every second of the day, better make sure you never have a heart attack and that you never slip on ice or have a motor vehicle accident.
If you do decide to day trade, just know that I or someone like me is out there scooping up all the money you are dropping on the floor as you day trade. It would be quicker if you would just write me a check for the money. Hours per day losing little bits here and there will take you a lot of time. I could use a vacation and $10k would get me a cruise.
Please pick up a copy of The Intelligent Investor, by Benjamin Graham and an undergraduate accounting textbook. I won't get a vacation paid for by you, but you might get a vacation paid for by someone else. Cruises are nice.
Let's say I want to try buying some penny stocksI'd avoid that or this will be a pretty short term "hobby-job"