Help to choose the right bike multipurpose bike I spend about 45 mins everyday commuting (less than 2 miles) to work on a formal dress, shoes, carrying a backpack that consists of a laptop, charger and little more stationery (about 10-12 pounds, I guess), amd probably get groceries way back home (5 pounds of stuff or so)

During weekends, I run errands for about 3-10 miles each day. I own no car, no scooter, no other vehicle. The only mode of transport is by bus, train majorly, perhaps walk and live in a 2nd floor house (but I don't mind carrying it up a 45 degree stairs). I even like to go off road during weekends, but that seems to be asking for more, but it would be great to have a bike that will atleast allow me to reach a hiking spot (slight muddy roads etc).

So with these things on mind, and a budget of $200 (I can double if its worth it, as this is the way its going to be for next 5 years atleast), I've been browsing and looking at different posts here. Particularly its focused on UK products but I live in US, New York; and I feel the bikes specifically are different than those available here, and the pricing. But few other links pointed out me very well, especially Jeol's choice of scooter and bike. Other option is Dahon c7 folding bike

The choice of different options and the upside price really confuses as me, a first timer. I am a software engineer living in New Jersey and travelling to New York by PATH/Subway trains so anyone who is of the same commute, please share your current choice, and the take away from it.

I had a ligament tear a year ago on the right knee, recovering but still finding it tough to walk on formal shoes in particular, and more painful to run errands walking during weekends. Kindly cast your recommendations. I am looking for a few choices so I can narrow it down, but right now I am even unable to oversee what I would need exactly for my purpose, and the choice of geek transportation system is worth the price.

Update after a year of bike usage in New York City and then Southern California

I bought a Dahon Vitesse from Craigslist and used for about 6 months in NYC. It was fun, very useful for errands. The thing I hated is lifting the bike up-and-down on the Subways. The folder though small is not the light-weight stuff.

I had moved to SoCal, did not have a car and badly wanted some bike to get groceries and food (public transport is pretty bad - wait 1 hour for a bus). I again went for a Dahon, this time the D7 model, and a brand new one. Still the bike is useful but for the nature of the city I think I should have gone for a light weight full hybrid bike.

The Dahon folder is great to commute for up to 10 miles for me. Great for plains, not so for elevated areas.
From your question above, i would only suggest the following (doesn't mean I don't know about the other bikes):

Folding bike - for work and city/cycle lane/fairly normal surfaces only. You can also get away with usual city road hazards such as potholes and cracks (but not too extreme), also good weight support (e.g. laptop, clothes, etc.). You might find it a bit weird to suddenly switch to a folding from a normal road/hybrid/MTB. But overall, it is really great as my gf bought a Tern C8 last month(she is 5'4") and even I find it nice to ride (I am 6'3"). You can also carry it on the train and even on the aeroplane if you want. Some folding bike tyres are quite sturdy compared to hybrids so the bumps and holes can be ignored a lot more. I would still give a trial ride if I was you in order to be sure about the comfort. THIS IS QUITE PRACTICAL if you are just living a professional life and city-side commute with occasional shopping bags (about 6 kgs) behind you.

MTB (Mountain Bikes) - If you want it to use on a rougher surface as well as in the cities. They are a bit heavy, but can take poundings like no other. You could even go over some road kerbs that are raised by appx. 3-4 inches. I apologise to be mean, but if you are not young enough to handle the bike weight, you might feel it difficult to go around the hills with these heavy bikes. But if you think you can, Go for this one. My suspicion based on UK prices is that you can probably get a very good MTB compared even when you double the price (if you are lucky, you might get one with suspension springs too, COOOL).

It is also possible to attach some rack or similar thing behind your MTB so that you can carry weight such as your laptop and clothes to work. I never saw anybody doing it for MTB, but that really does not mean you cannot. 

Short answer is, if you are happy to sacrifice outdoor activity, folding bike is the answer. Otherwise, get an MTB, get rack, and voi la. 

Bear in mind that no matter what bike you buy, there is a maximum weight for that. I would recommend staying about 6-7 Kgs under the prescribed weight by the manufacturer/seller. It was never an issue for me anyway as I carried shopping on my folding and hybrid, about 6-7 kgs of shopping.

I am really sorry but cannot guide you about the US price. If any other user finds this answer suitable, but want to edit it to put the price information, be my guest. Normally, I would put the UK prices but this would be confusing as you said yourself that the prices and the types of bike vary in the US shops. 

Hope this helps. If you were interested in the brands at all: 
Folding - Dahon, Tern, Raleigh, Brompton (around $800 sometimes due to the high demand)
MTB - Jamis, Trek, Pinnacle, Raleigh (Off-road series), Fuji, Bianchi

The choice is now yours, If you think I can give you more information please post follow-up comments :)