The penguins won't be around in April, I am afraid. But there is still plenty to do around Punta Arenas, a city with a lot of history in Chile. Definitely go to one of the estancias for a Patagonian lamb lunch.
http://www.welcomepatagonia.com/travel/punta-arenas-activities-excursions.php

Thanks for the link Huentetu!

You might consider splitting your time perhaps part in Puerto Natales which puts you 3 hours closer one-way to Torres del Paine.

Also the ferry operated by 21 de Mayo from Puerto Natales to the Serrano and Balmaceda glaciers with a lunch stop at an estancia, leaves from Natales. I am not sure if they run in April.

http://www.turismo21demayo.cl/programas.htm

One of our favourite restaurants is in Punta Arenas....highly recommend La Luna! Pics here

http://lizandrichardsa.typepad.com/liz_and_richard_in_south_/2006/03/the_lake_distri.html

I agree about spliting your stay between Punta Arenas and Puerto Natales. Both cities could be good bases for day trips depending on what you would like to see and do.

I just got back from Chile and I much preferred Puerto Natales and Torres del Paine over Punta Arenas. I stayed at the costaustralis hotel in Puerto Natales which was really nice. Spent several days in Torres Del Paine which was the highlight of my trip

Punta Arenas downtown area was not worth seeing, many boarded up shops , graffiti, not many restaurants, could not even find a minimart or grocery store. I did enjoy the half day trip to Magdalena Island to see the penguins, and a half day kayaking trip from Punta Arenas.

My husband and I want to stay only in Punta Arenas as my daughter will be in port there for work so that is why I wanted to do daytrips out of there.Any tour companies you would recommend,hotels or restaurants? Thanks!

Comapa is a big tourist agency in P. Arenas that runs the trips to Magdalena

http://www.comapa.com/en/

I stayed at a nice B&B near the P. Arenas airport, they take you into town as needed.
Run by English teachers, very helpful/

http://www.lacasaescondida.cl/home.html

There is an article on Patagonia, including P. Arenas, in the travel section of the NY Times for Sunday, Jan. 6, 2013, that you probably can view online. ZZ

saving for me

You can't miss the National Reserve Magallanes, walk its trails and enjoy the most beautiful landscapes. You can navigate the Estrecho de Magallanes. There are many Museums as well.

In Punta Arenas you can eat traditional food, the seafood is delicious: you can go to "Sotito's" or to "Los Ganaderos".

In terms of activities, there are places to go trekking, kayaking, canopy, fishing and other outdoor activities, so it depends on what you want to do.