From Miraflores the Ruta Recomendable to take to Centro de Lima is the OM23 (blue line). Get on at Ovalo de Miraflores (Parque Kennedy) or anywhere along Avenida Arequipa.
The ride to Centro de Lima will take about 20-30 minutes and will cost S./1.20 if you get on at Ovalo de Miraflores or S./1.00 if you get on at Angamos or closer towards Centro de Lima. The price of the boleto (ticket) is somewhat arbitrary, so you may be charged anywhere between S./1.00 or S./1.50. Never pay more than S./1.50.
Get off at Avenida Grau for the Museo de Arte de Lima (MaLi). From here everything is within walking distance. The next block north is Real Plaza, a shopping center that includes Starbucks. The Sheraton Hotel is also here, as well as the Estacion Central for the Metropolitano.
If you dont like to walk and especially if you are going to the Plaza Mayor (Plaza de Armas), another option is to continue on the OM23 until the last stop before the bridge. In this case you get off at the Iglesia (church). From here it is a 4-block walk to the main square.
Alternative routes are the SO08 (yellow line) and the NO02 (light blue line). Both of them take a bit of a detour, but they will get you there. If you take the NO02, get off at Plaza Bolognesi and walk to the Museo de Arte de Lima (MaLi). If you take the SO08 it is best to get off at Congreso.
A serious alternative is to take the Metropolitano from Estacion Ricardo Palma (walking distance from Ovalo de Miraflores) or any other station and go to Estacion Central. This journey is faster, but less charming. It will cost a fixed price of S./1.50 and you will need a charge card. The card can be obtained in any estacion. You will need to charge it with a minimum of S./5.00 the first time. At Estacion Central you can either change to another Metropolitano going north for one or two more stops or you can walk from here through Plaza San Martin towards Plaza de Armas.