Because you specifically asked about winds and pressure, there is a fairly applicable rule of thumb. It's called Buys Ballot's Law. Basically, if the wind is to your back (coming behind you), and you're in the Northern Hemisphere, generally low pressure is to your left and high pressure is to your right. This graphic from http://www.maiamarinelli.com/ illustrates it:
However, do note that Buys Ballot is really an imperfect estimation. There's three big caveats/adjustments to consider:
[in all following description, replace left with right (and vice versa) for Southern Hemisphere]
- The Buys Ballot Relationship fundamentally relies upon the Earth's rotation, i.e. the always vaunted apparent force termed the Coriolis Effect. Coriolis actually causes wind NOT to flow towards low pressure, but instead along equal pressure contours. If it weren't for the Coriolis Effect, low pressure centers would quickly fill in with air, and we wouldn't have the complex weather that we have. That said, at the equator, where the differences in rotation with latitude are smallest, Buys Ballot no longer works as there's limited/no Coriolis. So the nearer the equator you are, the more low pressure would be more infront left, or even straight in front of you if wind is to your back.
- Friction also slightly imbalances the relationship near the ground, such that wind actually flows towards low pressure again. So once again, wind to your back may actually indicate the low pressure center is more to your front left than your left at ground level. If you were up off the ground, or out in a body of water, this friction adjustment would be minimized, and low pressure is indeed more to your left.
- Local effects, such as terrain (or buildings) definitely overwhelm the larger pattern at times. And because the Coriolis force isn't significant in smaller, more localized features, Buys Ballot's becomes shakier in those situations. The impetus from the broader wind flow does feed down to guide even pressure local features. So wind to your back may well be telling you that a smaller area of low pressure is somewhere between to your left and in front of you... but that low pressure could be local: a building... a thunderstorm... even a tornado. That said, as the pressure gradient gets greater, Coriolis is more and more marginalized, and the low pressure can be almost directly in front of you... and there are even rare circumstances where it is strong that the low can rotate backwards, and low pressure may be to your right. As far as I know, this scenario only can maintain itself at all in strong thunderstorms, with the quite rare antimesocyclones and anticyclonic tornadoes. However, perhaps it could also happen on the microscale, such as around buildings, but those circumstances are no within my area of knowledge.
So all that put together:
If indeed you can get away from those big buildings, are fairly removed from the regional impacts of mountains and smaller nearby terrain features, and ideally can escape areas with dense foliage... then if the wind is coming from behind you, you can be almost certain that large low pressure is to your left or front left (in the NH, right/front right in the SH)... if you can find the wind direction.
And if there isn't much wind? Well then you're probably fairly near a high pressure center! But that will make it fairly tough to diagnose exactly where high pressure centers/low pressure centers are in relationship to you.
(And if there is a great deal of wind... well maybe you should just get inside, and turn on your tv to find out when the big tornado/hurricane/winter storm is going to end!)
- You could also use a barometer to diagnose falling/rising pressure trends. Those indicate that a low/high is moving towards you. However, this doesn't tell you what direction the low or high is located [though you can often make an educated guess based upon predominant wind flow; most pressure systems come from the west in the mid-latitudes, which include much of the US/Europe/Asia].
- As gansub noted in the comments, you could watch how atmospheric conditions evolve, such as the cloud patterns/types. https://www.youtube.com/watch?v=tsD6zkBMmck is a reasonable description of what goes on around fronts, which could help alert you to incoming storms (both warm and cold fronts are dips of low pressure, and indicate a large low pressure system is coming). The continuing lack of cloudcover might be an indication of high pressure in the vicinity.