Briefly, I will try to give you some info about what you can do in Paraguay. |
Asuncion: walk the city centre, more info on http://realtravel.com/asuncion-reviews-a3629082.html. Visit the Museo del Barro for indigenous art and objects, the Zoo and Botanical Gardens for the Natural History Museum with mommies and pickled strange animals and green spaces, the Villa Morra district for shopping centres and nightlife, try typical Paraguayan food in the Lido Bar or any other place: bori bori, chipa guazu, sopa paraguaya, pira caldo, payagua mascada, pastel mandi'o.
Visit Aregua for historic houses, the Ypacarai Lake, perfect hexagonal formations in Koi and Chorori Hills and ride the Train del Lago. More info on http://realtravel.com/aregua-reviews-a3847089.html and http://realtravel.com/asuncion-reviews-a3635968.html.
Check the Yaguaron town for a great church with Spanish Guarani baroco art, the museum of the Dr. Francia and the Yaguaron hill. http://realtravel.com/yaguaron-reviews-a3830126.html
Caves in Vallemi, Tagatija River for snorkelling and swimming with colourful fishes, Fort San Carlos 1806, all in the Concepcion department area.
Get a boat trip upriver from Asuncion. Visit Concepcion, Bahia Negra (Paraguayan Pantanal) and Fuerte Olimpo.
Jesuit remains in Trinidad and Jesus, both UNESCO World Heritage. Visit less known jesuit towns such as San Cosme y Damian http://realtravel.com/san_cosme_y_damian-reviews-a4003034.html, Santa Maria de la Fe with museum http://www.cockaigne.demon.co.uk/santamaria/santamariahome.html, Santiago in the Misiones Department.
Visit the Guaira region for the Ybytyrusu National Park with waterfalls, runic inscriptions in Ita Letra, german colonies and low range hills for mountainbiking, trekking, and adventure sports. Check http://realtravel.com/villarrica-reviews-a3690291.html and http://realtravel.com/guaira-reviews-a3791880.html.
Visit the Chaco for wilderness, wildlife, menno colonies, historic battlefields. There are bus conexions between Asuncion and Santa Cruz de la Sierra, Bolivia through this region.