The best way to travel to and around the The Bronx is on the MTA subway and bus. If you are traveling from Manhattan you will travel North of the city on the following subway lines; 1 & 2 (Westside), 4, 5, 6 (Eastside), A, C, B, D (Westside).
As for the bus, there are too many to list here. I recommend that you check out the MTA website for subway and bus lines and for any service interruptions which usually occur during the weekend and evening hours.
Taking the Metro North is an easy and fast way to travel to the Bronx (although limited sections) if you are coming from Grand Central.
You can travel to points north of Grand Central with the following stops:
The Harlem line: Melrose, Tremont, Fordham, Botanical Gardens, Williams Bridge and Woodlawn
The Hudson line: Morris Heights, University Heights, Marble Hill, Spuyten Duyvil and Riverdale.
Most of the time I visited The Bronx, I drove down from upstate NY. On a good day the trip would be a mere 70 minutes, but lets face it most days it was closer to 90. The only two bad things about driving are hitting traffic and paying the tolls on the thruway and Tappanzee Bridge. If you do drive to The Bronx, I suggest you fill up before you go so you won't have to buy gas down there, it's usually about 25 to 50 cents a gallon more expensive in The Bronx than it is upstate. I always bring something to drink with me in the car since heavy traffic can leave you stranded for an hour or more no where near a rest stop.
Bronx like the rest of NYC has a great system of buses servicing just about every corner of the island. At last count there were near 40 buses that can take you from one end of The Bronx to the other and back. The fare per ride is $2, $5 for express buses and children under 44 inches tall ride for free. If you ride the bus a lot your best best is to invest in one of the many unlimited and combination metro ride options.
Metro North has the Woodlawn station right across the street from where I live. Kind of cool as it is mostly cheap enough to take into the city. $4.50 off peak one way. $6.25 Peak. The best thing is on the weekends when it is $3.00 each way.
The Bus connects for free to the subway lines. Just need to use a metrocard. This provides the cheapest way of moving around the area and into the city. Several lines of the subway go into the Bronx. The 2, 4, 5 being closest for me where the Bx31, Bx16 and Bx34 busses connecting to them.
When Patrick and I made our first trip to The Bronx, we took the Metro North Railroad. I paid about $20 for a roundtrip ticket for myself and Patrick was free. The best thing about it was Patrick being able to look out the windows at the passing scenery. That was how he came to know the names of so many towns, rivers and land marks in the area. There are bathrooms on board for the weak of bladder, but I've never used them. The fare depends on where you board and depart, but your ticket is good for 3 months after date of purchase, so if you don't make it home on the same day it doesn't matter. Children under 5 are free and children traveling with a paying adult are no more than $1.00 each way.
The Bronx is also very fortunate to have several subways servicing the island. I've been on the 4 and 5 trains only and have no complaints about the ride. Actually the last time I rode the subway in The Bronx, I rode the 4 train with SES and some young 20 something kid tried to pick me up. It was funny since SES and I were drunk off our behinds. It costs $2 per ride to use the subway or $5 for each express ride. As with the buses, children under 44 inches tall ride for free.
Directions: Subway, D train to Fordham Road. the exit is on Grand Concourse and 188th and you will need to go one block towards Fordham road. You could walk down 188th all the way but I feel Fordham road is safer. (slightly uphill and to the north) Take a right on Fordham and walk downhill past all the clothes stores, past Fordham University (on left) and about a block after the White Castle at a gas station turn right onto Arthur Avenue.15 minutes.
Or take Metro North train from Grand Central Station in Manhattan (its more expensive but much faster) to Fordham Station You will take a left out of the station onto Fordham road past Fordham Univ. till Arthur avenue. 10 minutes maximum. This way saves you the walk through the crowds of people shopping on the Fordham Road towards the subway stop. It has a latin american feel, lots of people speaking in Spaish.
Driving, Deegan Expressway to Fordham road (rt) and same as before.
I am a firm believer that in order to really know an area you must walk it. In my experience, I haven't hit any seriously dangerous neighborhoods in The Bronx. Sure most folks won't look you in the eye as you walk by and many won't even return a simple good morning, but what the heck. I do not suggest walking out on your own at night no matter where you are in The Bronx, that's just plain old common sense.
The taxis in the Bronx aren't your typical yellow cabs found in Manhattan. They are usually Lincoln town cars with leather interior, and very comfortable. Most of the drivers speak Spanish as a first language, At least in this area around Fordham Road. I always had a good experience using these cabs and if you speak Spanish, even better.
How to know if the car is a cab...If the cab thinks you are looking for one they will honk the horn, they arent marked specifically always but on the license plate it will say NY T&L (taxi and livery). Most are Lincoln town cars like the one in the picture.
From Manhattan you take the green subway line uptown for the Bronx. I think line number 4 goes straight to Yankee Stadium. Remember, nearly other Yankee fan will be travelling this way so either leave in good time or be prepared for a busy train ride.
Subway, especially for tourists since traffic is almost always horrific. This is the station for the #1 that does down Broadway in the Bronx from Manhattan.
Nothing beats driving. Roads are full of huge potholes, drivers are crazy, everyone double parks and pedestrians are everywhere. It's like playing Frogger with your car as the frog. If you are a timid driver, DO NOT DRIVE HERE!
The MTA Bus cover the Bronx as well as Manhattan, Queens, Brooklyn & Staten Island. The fare for a subway or local bus ride is $2. The fare for an express bus ride is $4.
The fastest way to get to and around the bronx is by subway/train. There is the MTA New York City transit trains & the Metro North train, that stops at selective areas around the Bronx.