The hotel is north east of the Orchard Road area. From the main area of Orchard (i.e. the intersection of Orchard Road and Scotts Road), it is 1.5 miles or so to the hotel, up to you whether you would want to walk that, most of it is flat. A taxi would take under 10 minutes.

I think it would be about a 10 minute walk to the nearest subway stop (Novena), which is on the Orchard/Red line and it is only 2 stops to Orchard, so that would be a quick trip. (There are most likely buses as well, see http://www.smrt.com.sg for information. I don’t really know the bus lines in Singapore any longer.) You can also use this line to get downtown to Raffles Place and the museum area, as well as to the Marina area (for that monstrosity of a hotel) which is convenient as well.

The zoo is about 10 miles north west of your hotel. The zoo is also on the Orchard/Red line, and is 4 stops north of the Novena station. However, you can’t take the subway all the way to the zoo, you have to transfer to a bus, so between the walk to the Novena station, the subway ride, and the bus transfer time, it is going to be faster to take a taxi from the hotel to the zoo; this would be 20-30 minutes in the taxi. The zoo also has a dedicated express bus which goes from the Orchard Road area, see http://www.zoo.com.sg for timings and bus stops. The bus takes about an hour to get to the zoo from the Orchard Road area. You could also catch the express bus from the Serangoon Road area, which is closer to your hotel and which is a slightly shorter trip to the zoo. You would have to walk or take a taxi to get to this area, as otherwise you have to switch MTR lines, which just takes more time. (This area, however is part of Little India and is quite interesting for a walk and/or a meal. Far more interesting than Orchard Road, IMO.)

I see that the hotel is opening in early April. I know your trip to Singapore is at the end of April. Query whether you want to stay at a brand-new hotel. Things like the health club may not be open, and there may be teething issues with the physical plant or the staff. Just something to bear in mind. You might want to confirm whether the restaurants, health club, etc will be open by the time of your visit. The hotel also does not appear to have a pool, which is something one usually appreciates in Singapore. I think the rooms are going to be very small (you might want to confirm this with the hotel, they look like 25 square meters or less to me), but for 2 nights you can probably handle it, although if you have a lot of luggage for the rest of your trip, you may want to keep that in storage at the hotel. On the other hand, a brand new hotel will have new furniture, etc which can be nice.