There are basically four alternatives, of which the cheapest is the railway (a round trip from Retiro to Tigre costs about 70 cents of a dollar) and the subway (25 cents of a dollar per ticket including connections). The railway has many stations inside the city, but unless some of these is near where you are going, it would not be practical. Apart from this, during peak hours (6 to 9 in the morning and 6 to 8 in the evening) you will find it difficult to get onto a train, unless if you board it at the starting station. There are different railways in Buenos Aires, of which the Mitre railway is the best, and of the 3 branches of the Mitre railway, the best one is the one that goes to Tigre (the Paraná Delta) where you arrive after nearly one hour travel. You might want to get off the train at Acassuso and walk the most exclusive area of Metropolitan Buenos Aires, where there are some fantastic residences overlooking the River Plate at a distance. Or even at San Isidro, where you will find boating clubs along the riverside.
The other branches of the Mitre railway go to José León Suarez and to Florida, but there is nothing special to see along those lines. The San Martin railway goes to José C. Paz and the Belgrano railway follows a similar route. These 3 first railway lines leave from the Retiro station, quite near to the long distance bus station, and nearly in front of the Sheraton hotel (Plaza San Martin). The Sarmiento railway goes from Plaza Once to Moreno, both pretty unsafe areas, that has nothing worthwhile visiting. The Roca railway goes from Plaza Constitución (another unsafe area) to Temperley and beyond and La Plata (a higher rate applies if you travel to La Plata), and the Federico Lacroze railway goes from Chacarita to Campo de Mayo. Most of these railways have suburban connections, where higher rates apply. But the only line that has tourist attractions all along the way is the Mitre railway branch that goes to Tigre. First you will see the Avenue Libertador skyline on the left hand side, then the Palermo parks on the right hand side, tennis courts at Lisandro de la Torre, the suburban areas of Belgrano, Nuñez and Rivadavia, and then will start going through the Vicente López and Olivos areas, including the Presidential Residence, after which the really nice area starts (La Lucila, Martínez and Acassuso. Getting off at any of these stations and walking around should be quite safe during daytime. But use your common sense: don't show your cameras and camcorders when you are not using them, and do not speak aloud in English. You will not be recognized as a foreigner if you do not open your mouth. There is a high percentage of European population and their descendants in Argentina.
THE SUBWAY/METRO SYSTEM. Line A connects Plaza de Mayo (Government House and City Hall) with Congreso (the Congress) and all the way to Plaza Once (Sarmiento railway) and Primera Junta. Beyond the Congress, it goes through mostly middle class areas, where there are no special attractions worthwhile visiting. Line B connects the Central Post Office (near Puerto Madero, a fashionable area) with Chacarita (Federico Lacrozze), all the way up Corrientes Avenue,.where it connects with the Federico Lacrozze railway that goes to Campo de Mayo There is nothing special to see here. Chacarita is the main cemetery in Buenos Aires. If you get on to the train, and get off at Facultad de Agronomía, you will see a park and some clubs, but I should say that the main attractions are in the Northern part of Buenos Aires (along avenues Santa Fe and Cabildo -Barrio Norte, Palermo, Belgrano and beyond). Line C connects the railway stations of Retiro and Plaza Constitución and connects with lines B and C at Diagonal Norte, just below the Obelisk, with line A at Avenida de Mayo, and with line E at Independencia. It runs mostly along the Nueve de Julio Avenue, and is the shortest subway line. Station Diagonal Norte is near the Republica, Gran Hotel Argentino, Colon and Panamericano hotels, and just below avenue Corrientes (theaters) and Lavalle street (cinemas). It is also a couple of blocks away from the Colon theater (the culture corner of Buenos Aires). Line D goes from Plaza de Mayo (really from Florida street) all the way to Palermo and Belgrano, two areas that are worthwhile visiting. The Alto Palermo shopping is near the Bulnes station, the Palermo parks are next to the Plaza Italia Station, and the Belgrano shopping area is next to the Juramento station. One of the hotels I recommended (Mordomo) is two blocks away from the last station (Congreso de Tucumán). This line connects at Florida station with lines A and E, and at Carlos Pellegrini station with lines B and C. Line E goes mostly along Independencia avenue, but there is nothing special to see along its route. There are over 500 local bus lines in the city of Buenos Aires, and it would be impossible to give an overview of these. At any news stand you can buy a bus line guide for about one dollar. Keep in mind however that line 60 goes to Tigre (Parana Delta) and lines 15, 29 and 64 go to the Boca area. Taxis have reasonable prices, but distances are long. Once they cross the limits of the city (General Paz avenue) a 100% surcharge applies, since they are not allowed to lift passengers outside the city of Buenos Aires. They charge an average rate of 1 dollar per mile, with an initial rate of some 70 cents of a dollar. Price would be 2 dollars per mile outside of the city. Taxis are more expensive in the suburban part of Metropolitan Buenos Aires, beyond the city limits. If you intend to go somewhere and come back, most remises do not charge the return trip, while taxis do. Keep this in mind. When arriving at the Buenos Aires airport, NEVER accept transportation offers from unknwown people, they could be thieves. Always go to the Remisse counter (Tienda León at Ezeiza and Universal at Aeroparque). They will charge you more, but you will be safe. There is also a remise stand at the Buenos Aires bus station. I never use their services, because they are more expensive, but if you want to play safe, it may be the best alternative for you.
All long distance bus companies in Argentina require identification documents for selling you a ticket. This is for your own safety, so always carry your documents with you when you are going to buy a bus ticket. Most long distance bus companies accept credit cards and some, like Andesmar and Via Bariloche, also sell their tickets over the Internet. I trust you will find this information useful.