If a traveller intends to stay in a place for more than four days, then he comes under the same ruling as a resident and he must offer the prayers in full from the moment he enters the city, and he must attend Jumu’ah prayer when the call for it is given.
It should be noted that the traveller is obliged to pray in congregation, like a resident, and you have done well by making this room a prayer-room where you can offer prayers in congregation. See the answer to question no. 21498.
Jumu’ah prayer is obligatory for you, but it is not permissible for you to pray Jumu’ah in the room which you have made a place for offering the five daily prayers, because the basic principle is that it is not prescribed for there to be multiple Jumu’ah prayers except in cases of necessity. The basic principle is also that if a person is in a city where Friday prayer is held, he must go to the prayer even if it is far away. Allaah has made things easy for you, as there are mosques near you, as you say, which are ten, twenty and thirty minutes away.
Al-Nawawi (may Allaah have mercy on him) said:
Al-Shaafa’i and his companions said: If there are forty or more adults in a city, then Jumu’ah is obligatory for each of them, even if the city is large and whether they can hear the call to prayer or not. There is scholarly consensus on this point. End quote from al-Majmoo’ (4/353). See also the answer to question no. 14564.
You have to advise those who are lazy and do not pray Jumu’ah, by quoting to them some of the ahaadeeth which issue a stern warning to the one who stays away from Jumu’ah prayer, such as the words of the Prophet (peace and blessings of Allaah be upon him): “Whoever misses three Jumu’ah prayers out of carelessness, Allaah will place a seal over his heart.” Narrated by Abu Dawood (1052), al-Tirmidhi (500), Ibn Maajah (1269) and Ibn Maajah (1125). Classed as saheeh by al-Albaani in Saheeh Abi Dawood.
May Allaah help us and you to do that which He loves and which pleases Him.
And Allaah knows best.