I would say that this is highly dangerous. It is against US and Canadian code to not have outside ventilation for any fuel-burning appliance in your home; that's your furnace, HWH and stove/oven, assuming all are NG or propane. It is only acceptable to have a "filter-only" vent hood for your stove if it's all-electric (which BTW is the case for every single apartment I've ever rented; gas appliances may be cheaper on utility bills in the US, but a gas stove is a huge fire hazard and general liability for any landlord).
The code is in place for a very good reason; not only can inefficient burning of fossil fuels produce carbon monoxide and smoke (both of which continue to cause damage long after you've reached fresh air), but even when these fuels burn ideally, they remove oxygen from the air and replace it with CO2. CO2 in itself is not toxic in the same way CO and soot smoke are; as soon as you reach fresh air the symptoms of CO2 asphyxia begin to dissipate, while soot and CO poisoning ("smoke inhalation") can kill you hours after you reach fresh air. However, the consumption of oxygen and production of CO2 in a space with inadequate ventilation is a double-whammy for anyone in the same space; the oxygen is being consumed so there's less of it even in upper strata of the room's air, and as the CO2 builds it settles downward in a "blanket", pushing oxygen up towards the ceiling and away from you.
As the CO2 level builds, your body's natural "inhale/exhale" reflexes go haywire in a Catch-22 condition called hypercapnia; your natural breathing while in a high-CO2 atmosphere actually increases the CO2 levels in your blood, but the only thing your body can do to reduce CO2 levels is breathe. So, you start hyperventilating, which only exacerbates the problem. Should you pass out from lack of oxygen, you will not wake up if someone else doesn't get you out of the room or get some ventilation of fresh air through it.
Your landlord is running illegal housing. However, he may not know it, so be nice at first. Follow standard procedure for maintenance requests, and ask the landlord to install a proper outside vent line for this fume hood. If he refuses or drags his feet, you can call in the city's Code Compliance officials, or federal HUD (Housing and Urban Development) representative, and they will MAKE the landlord comply. Depending on the terms of your contract, the landlord may be giving you a free out by not living up to his end, meaning you may be able to break the lease at no cost if this has gone on for some time with the landlord's knowledge and inaction.
Understand that the cheapest way for your landlord to fix the problem with tenants still occupying the units may well be to cap off the gas feed and replace all the gas cooktops with the cheapest electric setups he can find. If this was the reason you moved in, and you don't get a "free out" from this debacle, you may find yourself stuck with a spiral-coil POS.
Everybody wants to save money
Builders and utility companies are not in the business of wasting money, which means the main line will be as straight and as short as possible. This is a big help to you, since it will narrow your search. Walk out to the curb shut off, and look back at your house. Try to determine the straightest, shortest path between the curb shutoff and the house. Now you'll have a general idea of where the line enters the home.
Trace the line
In most cases utilities bury a tracer wire in the trench above utility lines, to make the lines are easier to locate later. If you call 811 (assuming you are in the US, though I believe this service is offered in other areas as well), they should be able to send somebody out to locate the line for you. This will show you the approximate path the line takes to the house.
Don't let pipes freeze
Because it's a water line, it will likely enter your house below the frost line. If you can determine the frost depth in your area, you'll have a more targeted area to search.
People are idiots
It's not uncommon for people to do dumb things, especially when they don't know how dumb they are. Water meters and shutoffs are ugly, and nobody wants them in their newly remodeled living space. It's possible that your valve has been walled up, and you'll have to remove some finish material to find it. Look in closets, and keep an eye out for access panels.
If only you had X-ray eyes
There are a few tools that can help you search a wall where you suspect the valve might be. A stud finder should be able to locate pipes in the walls, depending on the stud finder you buy. A metal detector will find anything metal, so that could also come in handy. If you've got a bunch of cash to throw around, a thermal camera may be able to actually see the pipe through the wall.
Where does service enter?
After reading the update to the question, and then reading through building code. It seems that it may be possible that there is not a shutoff valve where the line enters the building.
International Residential Code 2009
P2903.9.1 Service valve. Each dwelling unit shall be provided with an accessible main shutoff valve near the entrance of the water
service. The valve shall be of a full-open type having nominal
restriction to flow, with provision for drainage such as a bleed
orifice or installation of a separate drain valve. Additionally, the
water service shall be valved at the curb or property line in
accordance with local requirements.
According to this, there must be a shutoff valve "near the entrance of the service". However, in most cases the water meter has to be near the "entrance of the service" too. In your case, it may be that the "entrance of the service" is at the property line, and not at the building. So there may actually be no shutoff valve inside the house.
Best Answer
Yes, putting the gas service shut-off in the laundry room would be fine (though they are typically found behind the appliance). Remember, this is a service disconnect valve (for maintenance or replacement of the appliance) not an emergency disconnect valve (in the event of a gas leak). The "emergency disconnect valve" is at the meter since the first rule for gas leak safety is to exit the building.