Rishikesh tourist life takes place mostly in the areas on both sides of the Ganges between two suspension bridges - Ram Jhula and Laxman Jhula. References to places are often made with respect to the bridges as well. So knowing them well help to give you a better sense of orientation and also to immediately know where people are talking about.
There are a few areas in Rishikesh which are more important to tourists. These are areas with a higher concentration of hotels/guesthouses, restaurants, tourist shops, ashrams and yoga centers and therefore useful for tourists to know, especially if you plan to stay in Rishikesh for a longer period of time or if you are looking for long term rentals.
The other not as often visited area is what the locals refer to as the "market". This is not the shops and stalls you see between Ram and Laxman Jhula but some kilometers away from this area, where most locals carry out their daily life like shopping for groceries and household items. The market is not just a market area selling all kinds of goods and services, but also a rather big city area where most of Rishikesh's main business takes place. Local residential areas and very local temples and ashrams (meaning, hardly any non-indian tourists visit them) can be found here too. It is also the place where you will most likely encounter first if you take a bus to Rishikesh as the main bus stand is here.
Like any other place, knowing where these areas are and what they offer can help you solve simple daily life problems which could potentially cause plenty of headaches and unnecessary time spent. Take for example, where do you buy basic items like bedsheets and towels? What about house cleaning tools like pails and mops? Where can you find cheaper long term housing and which area is more accessible than others for your needs? If you are time constrained and want to do as much as you can in a short time, where is a more convenient location to stay?
Knowing these areas also helps you to understand the places that you hear about, especially from the locals and longer term stayers. As Rishikesh is a compact town where many places can be reached on foot or with a short autorickshaw ride, it is not all that difficult to understand where you are.